Abstract:
A system and associated methodology to directly measure the concentration of carbonate ions in seawater by ultraviolet absorbance spectroscopy. Metal ions are added to seawater and the absorbance spectra of the added ions are measured in the ultraviolet. The spectral absorbance (light attenuation) of ions such as divalent lead or copper in seawater is predominantly determined by the carbonate ion content of seawater. Through a knowledge of (1) the strength of association between carbonate and either divalent lead or divalent copper and (2) the spectral characteristics of these cations in seawater (e.g., Pb 2+  complexed solely as PbCO 3  and Pb 2+  complexed solely in the form of chloride complexes), it is possible to directly determine seawater carbonate ion concentrations from absorbance measurements at a variety of wavelengths in the ultraviolet. Using such procedures, carbonate ion concentrations can be directly measured, rather than calculated from other CO 2  system parameters such as pH and total dissolved inorganic carbon. Measurements of carbonate ion concentrations, and measurements of solution pH that also involve spectrophotometric procedures, will allow both types of measurements in a single, small, robust instrument. Furthermore, via simple thermodynamic calculations, conjugate measurements of carbonate and pH can then be used to calculate all carbon system parameters of interest, including the total concentration of dissolved inorganic carbon in seawater.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to currently pending U.S. Provisional Patent Application 60/914,384, entitled, “Sensor for Direct Measurement of Carbonate Ions in Sea Water”, filed Apr. 27, 2007, the contents of which are herein incorporated by reference. 
    
    
     FIELD OF INVENTION 
     This invention relates to sensors for deployment in saltwater environments. More specifically, this invention relates to sensors for the measurement of carbonate ions in seawater. 
     BACKGROUND OF THE INVENTION 
     Carbonate ion concentrations are important parameters in marine ecosystems. Investigations of the marine CO 2  system are commonly conducted through measurements of four primary variables: total dissolved inorganic carbon (C T ), total solution alkalinity (A T ), CO 2  fugacity (f CO2 ), and solution pH. Thermodynamic models link these four primary variables, whereby measurements of any two variables can be used to calculate the two remaining parameters (DOE, 1994. Handbook of Methods, Version 2, A. G. Dickson &amp; C. Goyet, eds. ORNL/CDIAC-74). These models also allow calculations of the concentrations of the individual forms of inorganic carbon in seawater: the dissolved concentrations of CO 2  and H 2 CO 2 , and the free plus ion paired concentrations of bicarbonate, HCO 3   − , and carbonate, CO 3   2− . Two of the directly measured and derived CO 2  system variables can be highlighted because of their special significance in evaluations of global carbon fluxes and the biogeochemistry of marine carbonates in general. CO 2  fugacity measurements are essential to descriptions of CO 2  exchange at the air sea interface (DOE, 1994; McGillis, W. R. and Wanninkhof, R.;  Mar. Chem.  2006, 100-108; Millero, F. J.  Chem. Rev.  2007, 107, 308-341), and carbonate ion concentrations are essential to evaluations of (a) the mineralization rates of marine calcifiers (Langdon, C. and Atkinson, M. J.,  I Geophys. Res.  2005, 110, C09S05, doi: 10.1 029/2004JC002576) and (b) the dissolution rates of calcite and aragonite (CaCO 3(S)  polymorphs) both on the seafloor and in the water column (Keir, R. S.  Geochim. Cosmochim. Acta.  1980, 44, 241-252; Morse, J. W.  Amer. J. Sci.  1978, 278, 344-355; Acker, J. G., et al.,  Geochim. et Cosmochim. Acta  1987, 51, 2171-2175). Rising atmospheric carbon dioxide concentrations over the past two centuries have led to increasing CO 2  uptake by the oceans (Royal Society, 2005, Ocean Acidification due to Increasing Atmospheric Carbon Dioxide.  Policy Document  12/05,  The Royal Society ). This process, which is decreasing the pH of the upper ocean, is reducing oceanic carbonate ion concentrations and thus the level of saturation of calcium carbonate (Broecker, W. S., et al.,  Science  1979, 206, 409-418; Feely, R. A., et al.,  Science.  2004, 305, 362-366; Orr, J. C., et al.,  Nature.  2005, 437, 681-686). If the trend continues, it will have a seriously negative impact on key marine organisms such as corals and some plankton (Kleypas et al, Impacts of Acidification on Coral Reefs and Other Marine Calcifiers: A guide for Future Research. Report of a workshop held 18-20 Apr. 2005, St. Petersburg Fla., sponsored by NSF, NOAA and U.S. Geological Survey. 88 pp). In view of the importance of carbonate ion concentrations ([CO 3   2− ] T ) to the oceans&#39; rapidly evolving carbonate system, it is then highly desirable to move ([CO 3   2− ] T  from the rank of derived CO 2  system variables to the list of primary measured variables. The present invention provides methods and associated systems to meet this important objective. 
     SUMMARY OF INVENTION 
     The present invention provides procedures for measurement of carbonate ion concentrations in seawater by direct spectrophotometric observations of metal ion complexation (e.g. Pb II ). Metal ions are added to seawater and the absorbance spectra of the added ions are measured in the ultraviolet. The health of coral reefs and calcareous plankton is strongly influenced by the carbonate saturation state of seawater. Calculations of carbonate saturation states currently require measurements of two CO 2  system parameters, such as pH and total dissolved carbon, plus thermodynamic calculations that relate carbonate ion concentrations to directly measured parameters. The present invention provides novel procedures for direct measurements of carbonate ion concentrations and saturation states in seawater. The spectral absorbance (light attenuation) of ions, such as divalent lead or copper, in seawater is predominantly determined by the carbonate ion content of seawater. 
     Measurements are obtained via ultraviolet spectroscopic observations of Pb II  spectra as the relative concentrations of PbCO 3   o  and an ensemble of lead chloride complexes vary in response to dissolved CO 3   2− . Measurement precision is enhanced by parameterization in terms of absorbance ratios. The PbCO 3   o  stability constant, and Pb II  molar absorbance ratios in seawater, were determined at 25° C. over a range of salinity between 36 and 20. The procedures taught herein are well suited to measurements throughout the normal range of carbonate ion concentrations in the oceans. Rapid equilibration rates for Pb II  carbonate complexation make the procedures described in this work well suited to rapid direct analysis in situ. 
     In a first aspect the present invention provides a method of measuring carbonate ion concentrations in seawater. The method includes the steps of adding a Pb II  to a sample of the seawater to produce a sample solution, spectrophotometrically measuring the absorbance of light passing through the sample solution at a plurality of wavelengths and computing the carbonate ion concentration in seawater based upon the absorbance ratio of the sample solution at the plurality of wavelengths. The measured ultraviolet absorbance of light is a function of the complexation in the sample solution of the added Pb II  with the carbonate ion of the seawater sample. 
     The spectrophotometric absorbance measurements can be obtained in the ultraviolet range. In certain embodiments of the method, one of the plurality spectrophotometric absorbance measurements used to calculate the absorbance ratio is measured at about λ=234 nm. Further embodiments utilize a second absorbance measurement of the plurality of spectrophotometric absorbance measurements used to calculate the absorbance ratio measured in the range of at about λ=240 nm. to about λ=260 nm. In additional embodiments the spectrophotometric absorbance measurements are measured at about λ=234 nm. and about λ=250 nm. 
     In a second aspect the present invention provides a method of measuring carbonate ion concentrations in an aqueous media. The method includes the steps of adding a metal ion species to a sample of the aqueous media to produce a sample solution, spectrophotometrically measuring the absorbance of light passing through the sample solution at a plurality of wavelengths and computing the carbonate ion concentration in aqueous media based upon the absorbance ratio of the sample solution at the plurality of wavelengths. The measured ultraviolet absorbance of light is a function of the complexation in the sample solution of the added metal ion species with the carbonate ion of the aqueous media. 
     In certain embodiments the added metal ion species can be a lanthanide metal, an actinide metal, Yttrium, Pb II  or Cu II . In this and other aspects the lanthanide metal can be selected from the group La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu. In certain aspects the actinide metal can be uranium. In an advantageous embodiment the metal ion species is Pb II  and the absorbance measurements are obtained as absorbance ratios measured at about λ=234 and about λ=250. The aqueous media measured can be an aqueous media characterized by salinity. The salinity can be in the range of between about 20 and about 36. In an advantageous embodiment the aqueous media is seawater. 
     In a third aspect the present invention provides a method of measuring salinity in seawater. The method can include the steps of adding a metal ion species to a sample of the seawater to produce a sample solution, spectrophotometrically measuring the absorbance of light passing through the sample solution at a plurality of wavelengths and computing the salinity in the seawater media based upon the absorbance ratio of the sample solution at the plurality of wavelengths. The measured ultraviolet absorbance of light is a function of the complexation in the sample solution of the added metal ion species with carbonate ions of the seawater sample; 
     The spectrophotometric absorbance measurements can be obtained in the ultraviolet range. In certain embodiments the added metal ion species can be Pb II  or Cu II . In an advantageous embodiments the metal ion species is Pb II  and the absorbance measurements are obtained as absorbance ratios measured at about λ=234 and about λ=250. In certain embodiments of the method, one of the plurality spectrophotometric absorbance measurements used to calculate the absorbance ratio is measured at about λ=234 nm. Further embodiments utilize a second absorbance measurement of the plurality of spectrophotometric absorbance measurements used to calculate the absorbance ratio measured in the range of at about λ=240 nm. to about λ=260 nm. In additional embodiments the spectrophotometric absorbance measurements are measured at about λ=234 nm. and about λ=250 nm. 
     In a fourth aspect the present invention provides an apparatus for measuring carbonate ion concentrations in seawater. The apparatus includes (i) a metal ion addition module for the addition of metal ion species to a sample of seawater and (ii) a spectrophotometric module for the spectrophotometric measurement of the attenuation of light passing through a resulting sample solution containing the added metal ion. The measured attenuation of light is a function of the carbonate ion concentration of the seawater sample. 
     In a fifth aspect the present invention provides a method of measuring salinity or chloride ion concentrations in an aqueous media. The method includes the steps of adding a metal ion species to a sample of the aqueous media to produce a sample solution, spectrophotometrically measuring the absorbance of light passing through the sample solution at a plurality of wavelengths and computing the salinity or chloride ion concentration in aqueous media based upon the absorbance ratio of the sample solution at the plurality of wavelengths. The measured ultraviolet absorbance of light is a function of the complexation in the sample solution of the added metal ion species with the carbonate ion of the aqueous media. In certain embodiments the added metal ion species can be a lanthanide metal, an actinide metal, Yttrium, Pb II  or Cu II . 
     In a sixth aspect the present invention provides an additional method of measuring carbonate ion, salinity or chloride ion concentrations in an aqueous media. The method includes the steps of adding a metal ion species to a sample of the aqueous media to produce a sample solution, spectrophotometrically measuring the fluorescence of light in a sample solution at a plurality of applied wavelengths and computing the carbonate ion, salinity or chloride ion concentration in aqueous media based upon the fluorescence ratio of the sample solution at the plurality of wavelengths. The measured ultraviolet absorbance of light is a function of the complexation in the sample solution of the added metal ion species with the carbonate ion of the aqueous media. As indicated more fully below, salinity and/or chloride ion concentration are found to vary in accordance with the complexation of carbonate ions with the added metal ion species. In certain embodiments the added metal ion species can be a lanthanide metal, an actinide metal, Yttrium, Pb II  or Cu II . 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a fuller understanding of the invention, reference should be made to the following detailed description, taken in connection with the accompanying drawings, in which: 
         FIG. 1  is a graph showing the Pb II  UV absorbance spectra in seawater at S 35.87 and 25° C. as a function of pH. 
         FIG. 2  is a graph showing the Pb II  UV absorbance spectra of acidified seawater (25° C., pH=3.73) at four selected salinities. 
         FIG. 3  is a graph showing salinity dependence of PbCO 3   0  formation constant at 25° C. 
         FIG. 4  is a graph showing salinity dependence of  250 ε Pb  and  250 ε PbCO3  at 25° C. 
         FIG. 5  is a graph showing salinity dependence of  234 ε Pb  and  234 ε PbCO3  at 25° C. 
         FIG. 6  is a graph showing the absorbance ratio of Pb II  in acidified seawater at 234 and 250 nm:  250 A/ 234 A ( 250 ε Pb / 234 ε Pb ) as a function of salinity. 
         FIG. 7  is a graph showing salinity dependence of e 1  at 25° C. 
         FIG. 8  is a graph showing salinity dependence of e 2  at 25° C. 
         FIG. 9  is a graph showing salinity dependence of e 3  at 25° C. 
         FIG. 10  is a graph showing the results obtained for log {( CO3 β 1 )/(e 2 )} using equation (20). 
         FIG. 11  is a graph showing the results obtained for e 1  using equation (20). 
         FIG. 12  is a graph showing the residuals ([CO 3   2− ] observed −[CO 3   2− ] predicted ) plotted as a function of [CO 3   2− ] observed  for the least squares analyses using equation (20). 
         FIG. 13  is a graph showing the absorbance spectra obtained after is Cu II  added to seawater to obtain copper concentration on the order of 5 micromolar. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The present invention provides procedures for measurement of carbonate ion concentrations in seawater by direct spectrophotometric observations of Pb II  complexation. The health of coral reefs and calcareous plankton is strongly influenced by the carbonate saturation state of seawater. Calculations of carbonate saturation states currently require measurements of two CO 2  system parameters, such as pH and total dissolved carbon, plus thermodynamic calculations that relate carbonate ion concentrations to directly measured parameters. The present invention provides novel procedures for direct measurements of carbonate ion concentrations and saturation states in seawater. Measurements are obtained via ultraviolet spectroscopic observations of Pb II  spectra as the relative concentrations of PbCO 3   o  and an ensemble of lead chloride complexes vary in response to dissolved CO 3   2− . Measurement precision is enhanced by parameterization in terms of absorbance ratios. The PbCO 3   o  stability constant, and Pb II  molar absorbance ratios in seawater, were determined at 25° C. over a range of salinity between 36 and 20. The procedures taught herein are well suited to measurements throughout the normal range of carbonate ion concentrations in the oceans. Rapid equilibration rates for Pb II  carbonate complexation make the procedures described in this work well suited to rapid direct analysis in situ. 
     A variety of metals in seawater, including lead (Byrne, R. H.  Nature  1981, 290, 487-489), copper (Byrne, R. H. and Miller W. L.  Geochim. et Cosmochim. Acta  1985, 49, 1837-1844), Yttrium, the lanthanides (Cantrell, K. J. and Byrne R. H.  Geochim. et Cosmochim. Acta  1987, 51, 597-605) and various actinides (Byrne, R. H.  Geochem. Trans.  2002, 3, 11-16) have inorganic speciation schemes that are strongly dominated by carbonate complexation. It is envisioned that these metals from these groups (i.e. Yttrium and rare earth metals—lanthanides (La III , Ce III , . . . through Lu III ) and actinides; with respect to actinides it is envisioned that uranium would be a preferable metal species to employ) could perform as substitutes for lead or copper in the methodology. Among these metals, the speciation of Pb II  and Cu II  has been examined directly by ultraviolet absorbance spectroscopy in natural seawater (Byrne, 1981; Byrne and Miller, 1985). Since ultraviolet absorbance spectra are strongly influenced by the carbonate ion concentration of seawater, it follows that observations of Pb II  and Cu II  absorbance spectra can be used to directly determine seawater carbonate ion concentrations. As a means of achieving high precisions in such determinations, procedures have been developed that involve measurements of absorbance ratios rather than absolute absorbance. The techniques applied can be compared and contrasted with those for seawater pH measurements, which achieve precisions on the order of 0.0004 pH units (Robert-Baldo, G. et al.  Anal. Chem.  1985, 57, 2564-2567; Byrne, R. H.  Anal. Chem.  1987, 59, 1479-1481; Byrne, R. H. and Breland, J. A.  Deep - Sea Res . A. 1989, 36, 803-810; Clayton, T. D. and Byrne, R. H.  Deep - Sea Res . A. 1993, 40:2115-2129). Whereas spectrophotometric observations of sulfonphthalein acid/base equilibria are utilized for seawater pH measurements, spectrophotometric observations of metal ion complexation can be used to quantify anion concentrations in seawater. Lead is especially well suited to such measurements because (a) PbCO 3   0  and a variety of Pb II  chloride complexes have dissimilar absorbance spectra in the ultraviolet, and (b) species other than PbCO 3   0  and chloride complexes appear to be insignificant over a wide range of salinities in natural seawater. In this work, Pb II  formation constants and molar absorbance ratios required for direct determinations of carbonate ion concentrations in seawater are characterized at 25° C. as a function of salinity. In addition to development of procedures for measurement of carbonate ions and carbonate saturation state, it is shown herein that measurements of Pb II  absorbance ratios in acidified seawater can be used to determine seawater salinity with a precision on the order of ±0.1 salinity units. As an alternative to measuring absorbance, measurements of fluorescence could be employed to determine carbonate ion concentrations, salinity or chloride ion concentration. It is further envisioned that fluorescence measurements could be compared as fluorescence ratios to perform the calculations to determine parameters such as concentration. The procedures described in this work are suitable for rapid autonomous in-situ monitoring of carbonate ion concentration in seawater. 
     Theoretical Description 
     The PbCO 3   0  formation reaction in seawater,
 
(Pb 2+ ) T +(CO 3   2− ) T             (PbCO 3   0 ) T ,  (1)
 
can be quantitatively described with an equilibrium constant of the following form:

                     CO3   ⁢   β1     =         [     PbCO   3   0     ]     T           [     Pb   T     ]     ⁡     [     CO   3     2   -       ]         T   ⁢           ⁢                    (   2   )               
where [Pb T ] represents the total concentration of Pb(II) species other than PbCO 3   0  in seawater, principally Pb 2+ , PbCl + , PbCl 2   0  and PbCl 3   −  and minor amounts of PbSO 4   0 ; [CO 3   2− ] T  is the sum concentration of free and ion paired carbonate (CO 3   2− , NaCO 3   − , MgCO 3   0  and CaCO 3   0 ); and [PbCO 3   0 ] T  represents the sum concentration of PbCO 3   0  and potentially significant mixed ligand complexes such as PbCO 3   0 Cl − . The absorbance of Pb II  in seawater can be described using the following equation (Byrne, 1981; Soli, A. L. et al.  Mar. Chem.  2008, (in-press)):
   λ   A =( λ ε Pb + λ ε PbCO3 CO3 β 1 CO 3   2− ] T )/(1+ CO3 β 1 [CO 3   2− ] T )  (3) 
where  λ A is the absorbance of Pb II  at wavelength λ,  λ ε PbCO3  is the molar absorbance of (PbCO 3   0 ) T  at wavelength λ,  λ ε Pb  is the molar absorbance of (Pb) T  at wavelength λ and  CO3 β 1  is the formation constant of PbCO 3   0  as defined in equation (2). Equation (3) can be used to describe the dependence of Pb II  absorbance data ( λ A) on [CO 3   2− ] T  and determine an internally consistent set of values for  λ ε Pb ,  λ ε PbCO3  and  CO3 β 1 .
 
     Use of equation (3) at wavelengths and allows carbonate ion concentrations, [CO 3   2− ] T , to be directly calculated from observations of absorbance ratios:
 
 R=   λ2   A/   λ1   A =( λ2 ε Pb + λ2 ε PbCO3 CO3 β 1 [CO 3   2− ])/( λ1 ε PbCO3 CO3 β 1 [CO 3   2− ])  (4)
 
     Rearrangement of equation (4) results in the following equation:
 
−log [CO 3   2− ]=log  CO3 β 1 +log(( R−e   1 )/( e   2   −R·e   3 ))  (5)
 
where e 1 , e 2 , and e 3  are Pb II  molar absorbance ratios:
 
 e   1 = λ2 ε PbCO3 / λ1 ε PbCO3   , e   2 = λ2 ε Pb / λ1 ε PbCO3   , e   3 = λ1 ε Pb / λ1 ε PbCO3   (6)
 
     The form of equation (5) is analogous to that which has been used for highly precise measurements of seawater pH from observations of sulfonephthalein absorbance in seawater (Robert-Baldo et al, 1985; Byrne, 1987; Byrne and Breland, 1989; Clayton and Byrne, 1993). 
     At sufficiently low pH, equation (4) can be written as:
 
 R=   λ2   A/   λ1   A=   λ2 ε Pb / λ1 ε Pb   (7)
 
     Characterizations of the molar absorptivities of individual species of Pb II  can be used to directly determine the relative concentrations of Pb 2+ , PbCl + , PbCl 2   0  and PbCl 3   −  in both synthetic solutions and seawater. Since the relative concentrations of these species are directly dependent on the chloride concentrations in synthetic solutions and seawater, it follows that Pb II  absorbance ratios at low pH are directly dependent on salinity. In addition to developing a direct means of determining carbonate ion concentrations via equation (5), it is shown herein that observations of Pb II  absorbance ratios at low pH allow calculations of seawater salinity with a precision somewhat better than ±0.2%. 
     Methods and Procedures 
     Equation (5) can be used to determine carbonate ion concentrations via direct measurements of Pb II  absorbance ratios, and characterizations of  CO3 β 1 , e 1 , e 2 , and e 3 . Observations of Pb II  absorbance spectra at salinities typical of open ocean seawater (S=35.87) reveal isosbestic points near 234 nm ( FIG. 1 ). On this basis, one of the two wavelengths chosen for absorbance observations was λ 1 =234 nm. Although use of shorter wavelengths is desirable as a means of increasing sensitivity to formation of PbCO 3   0 , small absorbance contributions from carbonate ions at shorter wavelengths make interpretations of absorbances at λ&lt;234 nm less direct. In view of the substantial absorbance variations between 240 and 260 nm ( FIG. 1 ), the second of the two wavelengths chosen for absorbance ratio observations was λ 2 =250 nm. 
     Measurements of log  CO3 β 1  in this work were obtained using equation (3) and observations of  250 A and [CO 3   2− ] T  in seawater samples at constant salinity and constant temperature. Along with measurements of log  CO3 β 1 , these measurements also produced paired characterizations of  250 ε Pb  and  250 ε Pb CO3 . Paired characterizations of  234 ε Pb  and  234 ε Pb CO3  were obtained from measurements of  234 A and [CO 3   2− ] T  using equation (3), and the log  CO3 β 11  values determ 234 ε Pb  and  250 ε Pb  were obtained from  λ A observations at low pH ( FIG. 2 ). The molar absorbance ratios e 1 , e 2 , and e 3  in equation (5) were then determined from these paired molar absorbance characterizations as follows:
 
 e   1 =( 250 ε PbCO3 / 250 ε Pb )×( 234 ε Pb / 234 ε PbCO3 )×( 250 ε Pb / 234 ε Pb )  (8)
 
 e   2 =( 234 ε Pb / 234 ε PbCO3 )×( 250 ε Pb / 234 ε Pb )  (9)
 
 e   3 =( 234 ε Pb / 234 ε PbCO3 )  (10)
 
     All chemicals used were analytical reagent grade. PbCl 2  and NaHCO 3  were from Sigma-Aldrich. HCl (1.000 M) was from J. T. Baker. The seawater used in this study was collected from the Gulf of Mexico. Seawater salinity was measured with an SBE 49 CTD (Seabird). Seawater samples at various salinities were prepared by dilution with Milli-Q water. Absorbance measurements were obtained using quartz optical cells in an HP 8453 spectrophotometer. The temperature of the samples in the optical cells was controlled (25±0.05)° C. with a Neslab refrigerating circulator and a water-jacketed spectrophotometric cell holder. 
     Seawater alkalinity was determined using the spectrophotometric method of Yao and Byrne (1998) which is precise to better than 1 μmol/kg. Seawater (140.0 g) was added gravimetrically to an open top optical cell which, in turn, was positioned in the thermostated cell holder. Sample pH was measured using an Orion Ross-type pH electrode (No. 800500) connected to an Orion pH meter (Model 720A) in the absolute millivolt mode. Nerstian behavior of the pH electrode was confirmed via titrations of 0.7 molal NaCl solutions with concentrated HCl. The electrode was calibrated on the total hydrogen ion concentration scale through measurements in natural seawater whose pH was determined by simultaneous spectrophotometric observations of thymol blue absorbance ratios (Zhang and Byrne, 1996). 
     Through addition of NaHCO 3 , the alkalinity of each seawater sample was increased to values approximately double those of natural seawater (final alkalinity ˜4.0 millimolal). After each seawater sample was thermally equilibrated, a reference spectrum was taken and 1.05 ml of a 0.001 mol/kg PbCl 2  stock solution was added to the sample (final [Pb II ] T ˜7.5 μmol kg −1 ). An absorbance spectrum was then taken along with a potentiometric measurement of pH. The sample was subsequently titrated with standard HCl using a Gilmont micrometer syringe. HCl additions were quantified gravimetrically. Pb II  absorbance, alkalinity and pH were recorded for each titration point. Sample alkalinity was calculated by accounting [CO 3   2− ] T  from alkalinity and pH utilized the total H +  scale dissociation constants of Dickson and Millero (1987) that were derived from the data of Mehrbach et al. (1973). Non-linear least squares parameter estimates of  λ2 ε Pb ,  λ2 ε PbCO3  and  CO3 β 1  were obtained using equation (3) and paired values of  λ A and [CO 3   2− ] T . Calculations of [CO 3   2− ] T  that accounted for minor contributions of PbCO 3   o  to carbonate alkalinity did not cause significant changes in derived values of  λ2 ε Pb ,  λ2 ε PbCO3  and  CO3 β 1    
     Absorbance contributions of CO 3   2−  at short wavelengths were examined by performing titration experiments without addition of Pb II  to samples. Observations of well defined isosbestic points at λ=234 nm demonstrate that these corrections are very small at the wavelengths utilized in this work. The dependence e 1 , e 2 , and e 3  on salinity were described via quadratic functions. 
     Pb II  absorbance measurements in acidified seawater (pH˜3.7, [Pb] T ˜7.5 μmol kg −1 ) were used to determine  λ ε Pb  values at λ=234 and 250 nm. Absorbances, in this case, were measured against a reference solution of acidified seawater that contained no lead. The absorbance ratios obtained in these experiments ( 250 ε Pb / 234 ε Pb ) were used in determinations of e 1  and e 2  as described above, and were also used in a least squares quadratic regression that allows salinity (S) to be calculated from  234 A/ 250 A observations at low pH. 
     Example 1 
     Salinity Dependencies of Pb II  Molar Absorptivities and the PbCO 3   0  Formation Constant 
     
       
         
               
             
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 PbCO 3   o  formation constant ( CO3 β 1 ),  250 ε Pb , and 
               
               
                   250 ε PbCO3  as a function of salinity at 25° C. 
               
             
          
           
               
                 Salinity 
                 log  CO3 β 1   
                   250 ε Pb   
                   250 ε PbCO3   
               
               
                   
               
               
                 35.87 
                 4.070 ± 0.030 
                 0.2584 ± 0.0021 
                 0.0900 ± 0.0021 
               
               
                 34.50 
                 4.140 ± 0.028 
                 0.2504 ± 0.0026 
                 0.0973 ± 0.0018 
               
               
                 32.50 
                 4.151 ± 0.026 
                 0.2382 ± 0.0021 
                 0.0895 ± 0.0019 
               
               
                 30.00 
                 4.249 ± 0.021 
                 0.2259 ± 0.0016 
                 0.0875 ± 0.0014 
               
               
                 27.50 
                 4.290 ± 0.024 
                 0.2175 ± 0.0021 
                 0.0770 ± 0.0014 
               
               
                 25.00 
                 4.443 ± 0.028 
                 0.2027 ± 0.0024 
                 0.0768 ± 0.0013 
               
               
                 22.50 
                 4.559 ± 0.018 
                 0.1841 ± 0.0015 
                 0.0732 ± 0.0006 
               
               
                 20.00 
                 4.711 ± 0.022 
                 0.1697 ± 0.0016 
                 0.0674 ± 0.0008 
               
               
                   
               
             
          
         
       
     
     Estimates for  CO3 β 1 ,  250 ε Pb  and  250 ε Pb CO3  obtained using equation (3) are given in Table 1 and are shown graphically in  FIGS. 3 and 4 . Over a salinity range between S=20 and S=36, the dependence of the PbCO 3   0  formation constant on S at 25° C. ( FIG. 3 ) can be described as:
 
log  CO3 β 1 =6.574−0.1235 S+ 1.514×10 −3   S   2   (11)
 
with a ±0.023 standard error of estimation. The  250 ε Pb  and  250 ε PbCO3  values determined in this analysis exhibited a linear dependence on salinity:
 
 250 ε Pb =0.0632+5.446×10 −3   S   (12)
 
 250 ε Pb CO3 =0.0342+1.692×10 −3   S   (13)
 
     
       
         
               
             
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                   234 ε Pb  and  234 ε PbCO3  as a function of 
               
               
                 salinity at 25° C. 
               
             
          
           
               
                 Salinity 
                   234 ε Pb   
                   234 ε PbCO3   
               
               
                   
               
               
                 35.87 
                 0.2928 ± 0.0141 
                 0.3210 ± 0.0022 
               
               
                 34.50 
                 0.2911 ± 0.0116 
                 0.3190 ± 0.0026 
               
               
                 32.50 
                 0.2894 ± 0.0128 
                 0.3191 ± 0.0006 
               
               
                 30.00 
                 0.2904 ± 0.0097 
                 0.3101 ± 0.0005 
               
               
                 27.50 
                 0.2969 ± 0.0115 
                 0.2924 ± 0.0009 
               
               
                 25.00 
                 0.2954 ± 0.0111 
                 0.2819 ± 0.0012 
               
               
                 22.50 
                 0.2886 ± 0.0057 
                 0.2696 ± 0.0022 
               
               
                 20.00 
                 0.2874 ± 0.0078 
                 0.2511 ± 0.0035 
               
               
                   
               
             
          
         
       
     
     The  234 ε Pb  and  234 ε PbCO3  values determined using the log  CO3 β 1  results in Table 1 and absorbance observations at 234 nm are given in Table 2. The  FIG. 5  graphical depiction of these results shows that the dependence of  234 ε Pb  on salinity is linear while satisfactory descriptions of  234 ε PbCO3  require a quadratic term:
 
 234 ε Pb =0.2877+1.319×10 −4   S   (14)
 
 234 ε PbCO3 =0.0232+1.518×10 −2   S− 1.906×10 −4   S   2   (15)
 
     The salinity dependence for observations of ( 250 ε Pb / 234 ε Pb ) in acidified seawater (Table 3 and  FIG. 6 ) is well described by the following expression:
 
 250 ε Pb / 234 ε Pb =0.1931+1.062×10 −2   S− 3.852×10 −5   S   2   (16)
 
     
       
         
               
             
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Absorbance of Pb II  in acidified seawater (pH = 3.73): 
               
               
                   250 A/ 234 A ( 250 ε Pb / 234 ε Pb ) as a function of salinity at 25° C. 
               
             
          
           
               
                   
                 Salinity 
                   250 A/ 234 A ( 250 ε Pb / 234 ε Pb ) 
               
               
                   
                   
               
               
                   
                 20.00 
                 0.5906 
               
               
                   
                 21.25 
                 0.6135 
               
               
                   
                 22.50 
                 0.6308 
               
               
                   
                 23.73 
                 0.6593 
               
               
                   
                 25.00 
                 0.6863 
               
               
                   
                 26.25 
                 0.7069 
               
               
                   
                 27.50 
                 0.7327 
               
               
                   
                 28.75 
                 0.7526 
               
               
                   
                 30.00 
                 0.7778 
               
               
                   
                 31.24 
                 0.7987 
               
               
                   
                 32.50 
                 0.8231 
               
               
                   
                 33.75 
                 0.8448 
               
               
                   
                 34.50 
                 0.8603 
               
               
                   
                 35.00 
                 0.8688 
               
               
                   
                 35.61 
                 0.8788 
               
               
                   
                 35.87 
                 0.8830 
               
               
                   
                 35.87 
                 0.8818 
               
               
                   
                   
               
             
          
         
       
     
     Using the results that are summarized in equations (12) through (16), equations (8) through (10) can be used to calculate e 1 , e 2 , and e 3  at each salinity. The coefficients obtained in this manner are given in Table 4 and are depicted graphically in FIGS. ( 7 ), ( 8 ) and ( 9 ). 
     The salinity dependencies of e 1 , e 2 , and e 3  are then given as follows:
 
 e   1 =0.3447−6.662×10 −3   S+ 1.463×10 −4   S   2   (17)
 
 e   2 =0.7749−1.122×10 −2   S+ 3.331×10 −4   S   2   (18)
 
 e   3 =2.114−6.600×10 −2   S+ 9.036×10 −4   S   2   (19)
 
     
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 e 1 ( 250 ε Pb CO3 / 234 ε Pb CO3 ), e 2  ( 250 ε pb / 234 ε Pb CO3 ), and 
               
               
                 e 3  ( 234 ε Pb / 234 ε Pb CO3 ) as a function of salinity at 25° C. 
               
             
          
           
               
                   
                 Salinity 
                 e 1   
                 e 2   
                 e 3   
               
               
                   
                   
               
               
                   
                 35.87 
                 0.2938 
                 0.8009 
                 0.9068 
               
               
                   
                 34.50 
                 0.2890 
                 0.7841 
                 0.9131 
               
               
                   
                 32.50 
                 0.2828 
                 0.7619 
                 0.9263 
               
               
                   
                 30.00 
                 0.2766 
                 0.7381 
                 0.9498 
               
               
                   
                 27.50 
                 0.2721 
                 0.7182 
                 0.9825 
               
               
                   
                 25.00 
                 0.2694 
                 0.7024 
                 1.0262 
               
               
                   
                 22.50 
                 0.2687 
                 0.6908 
                 1.0835 
               
               
                   
                 20.00 
                 0.2701 
                 0.6838 
                 1.1588 
               
               
                   
                   
               
             
          
         
       
     
     Example 2 
     Determinations of CO 3   2−  Concentrations in Seawater 
     Equations (5), (11), and (17) through (19) permit direct measurements of [CO 3   2− ] T  from measurements of Pb II  ratios in seawater at 25° C. Equation (5) can, however, also be written in an alternative form, with a smaller number of parameters:
 
−log [CO 3   2− ] T =log {( CO3 β 1 )/( e   2 )}+log {( R−e   1 )/(1− Re   3   /e   2 )}  (20)
 
     This equation is advantageous for calculations of carbonate ion concentrations because (a) it reduces the number of parameterizations required for measurements: Using equation (20), ( CO3 β 11 )/(e 2 ) is determined as a single parameter, and (e 3 /e 2 ) is determined as one parameter; (b) the parameter (e 3 /e 2 ) can be precisely determined from direct measurements at low pH: It is directly determined from the absorbance ratios shown in  FIGS. 7-9  ((e 3 /e 2 )=( 250 A/ 234 A) −1 )); (c) using (e 3 /e 2 ) values determined at low pH, equation (20) can be used with paired [CO 3   2− ] T  and R observations to directly determine ( CO3 β 11 )/(e 2 ) and e 1 . The results of such analyses, using each of the data sets that were employed to develop equations (11) and (17) through (19) are given in Table 5 and are depicted graphically in  FIGS. 10 and 11 .  FIG. 12  shows the residuals, ([CO 3   2− ] T ) observed −([CO 3   2− ] T ) predicted , for each least squares analysis using equation (20). These results show that equation (20) can be used to satisfactorily predict [CO 3   2− ] r  over a wide range of conditions in seawater. The best least squares descriptions for the salinity dependencies of the parameters in equation (20) for 20≦S≦36 are given as follows:
 
log {( CO3 β 1 )/( e   2 )}=6.087−8.495×10 −2   S+ 9.360×10 −4   S   2   (21)
 
 e   1 =0.2215−5.554×10 −4   S+ 8.440×10 −5   S   2   (22)
 
( e   3   /e   2 )=3.061−8.730×10 −2   S+ 9.363×10 −2   S   2   (23)
 
     
       
         
               
             
               
               
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                 Obtained log{( CO3 β 1 )/(e 2 )} and e 1  using equation (20). (e 3 /e 2 ) 
               
               
                 used in equation (20) is the reciprocal of  250 A/ 234 A listed in Table 3. 
               
             
          
           
               
                 Salinity 
                 log{( CO3 β 11 )/(e 2 )} 
                 e 1   
               
               
                   
               
               
                 35.87 
                 4.202 
                 0.2957 
               
               
                 34.50 
                 4.304 
                 0.3217 
               
               
                 32.50 
                 4.328 
                 0.2909 
               
               
                 30.00 
                 4.426 
                 0.2867 
               
               
                 27.50 
                 4.400 
                 0.2582 
               
               
                 25.00 
                 4.542 
                 0.2609 
               
               
                 22.50 
                 4.650 
                 0.2538 
               
               
                 20.00 
                 4.773 
                 0.2449 
               
               
                   
               
             
          
         
       
     
     Example 3 
     Determinations of Seawater Salinity 
     The salinity measurements required for calculations of log {( CO3 β 1 )/(e 2 )}, e 1 , and (e 3 /e 2 ) are commonly available from either shipboard or in situ conductimetric measurements. When such is not the case, however, salinity can be calculated using the data that are shown in  FIGS. 7-9 :
 
 S=− 8.76+45.15 R+ 6.092 R   2   (24)
 
where R= 250 A/ 234 A and 20≦S≦36. The standard deviation for equation (24) estimates of salinity is ±0.06 salinity units. Thus, equation (24) provides seawater salinity estimates that are precise to approximately 0.2% over the normal salinity range of seawater.
 
     Example 4 
     Determination of Carbonate Ion Concentration Using Additional Metal Ion Species 
     Inorganic complexation of some ions in seawater, including lead and copper, is strongly dominated by formation of complexes with forms including PbCO 3   0  and CuCO 3   0 . [Byrne, R. H., Inorganic lead complexation in natural seawater determined by UV spectroscopy,  Nature , (1981) 290:5806, pgs. 487-489; Byrne, R. H and Miller, W. L., Copper (II) carbonate complexation in seawater,  Geochimica et Cosmochimica Acta , (1985) 49:8; 1837-1844] Furthermore, these complexes equilibrate with their component ions on time scales much less than one second and, importantly, can be monitored spectrophotometrically. For both copper and lead, it had been determined, by spectrophotometric means (ultraviolet spectroscopy), equilibrium constants (K) of the form:
 
 K=[MCO   3   0 ]/([M 2+ ] T [CO 3   2− ] T )
 
where M is Pb 2+  or Cu 2+ , and brackets denote total concentrations. These findings (spectrophotometric determinations of stability constants (K) for metal complexes) can then be used for inverse calculations leading to rapid direct observations of carbonate ion concentrations in seawater: Spectra of Pb 2+  or Cu 2+  in seawater in conjunction with the equilibrium constants described above allow direct calculation of carbonate ion concentrations, [CO 3   2− ] T . In spite of the desirability of such a capability, the possibility of this mechanism of determination of carbonate ion concentrations has not been noted previously.
 
     Using the procedure outlined above, carbonate ion concentrations can be determined in a rapid profiling mode (in the oceanic water column) through observations of lead or copper absorbance spectra in the ultraviolet. These absorbance measurements can be obtained as absorbance ratios in the same manner as used to achieve pH measurements precise to 0.0004 units (i.e. hydrogen ion concentrations precise to approximately 1/1,000). Rapid spectrophotometric pH measurements in conjunction with rapid carbonate concentration measurements can then be used to comprehensively characterize the marine CO 2  system with small, simple, in situ spectrophotometric devices. Spectrophotometric devices are sufficiently simple, relative to alternative technologies, to greatly facilitate carbon system measurements both in the field and in the laboratory. Devices based on the principles outlined above will allow direct determinations of carbonate saturation states, and can do so on time scales commensurate with very rapid profiling of the water column. 
       FIG. 13  shows absorbance spectra obtained after copper(II) is added to seawater to obtain copper concentrations on the order of 5 micromolar. 
     The increase in absorbance with increasing pH, with an absorbance maximum near 280 nanometers, is due nearly entirely to formation of CuCO 3   0 . This chemical complex is formed via the following reaction:
 
Cu 2+ +CO 3   2− =CuCO 3   0  
 
     The equilibrium constant for this reaction has been measured in seawater and has the form:
 
 K=[CuCO   3   0 ]/([Cu 2+ ] T [CO 3   2− ] T )
 
     In analogy with the use of pH indicators to determine solution pH (where pH=−log [H + ]) via observations of pH-indicator absorbance ratios, the following equation can be used to directly determine a solution&#39;s carbonate ion concentration.
 
 p CO 3   2− =−log [CO 3   2− ] T =log  K +log {( R−e   1 )/( e   2   +Re   3 )}
 
     Where K is an equilibrium constant (dependent on temperature, salinity and pressure), e 1  are molar absorbances (constants that are very weakly dependent on temperatures, salinity and pressure) and R is a directly measured absorbance ratio (R=A 2 /A 1 ) at wavelengths  2  and  1  (i.e. λ 2  and λ 1 ). In the graph shown in  FIG. 13 , A 2  and A 1 , measured at wavelengths near 280 nanometers and 230 nanometers, are approximately 0.083 and 0.04 at pH=8.2. therefore, at this pH, due predominantly to carbonate complexation, R=2.075. Inspection of The Figure shows that R values at these wavelengths decrease sharply at lower pH (lower carbonate ion concentration). As an example, at pH 4.4, when [CO 3   2− } is near zero, R is much smaller than one. 
     More advanced equations, including equations that consider many wavelengths simultaneously, can be used for this analysis. For greatest accuracy, minor influences can be considered from species such as CuOH +  and Cu(CO 3 ) 2   2− . 
     An advantage of this methodology is that it can be used to directly determine carbonate ion concentrations. Other methods for determining carbonate ion concentrations require measurements of two carbonate system variables plus a subsequent calculation. Thus, the method requires only one type of measurement. Another advantage of this methodology is its speed. Complexation of copper by carbonate ions is essentially instantaneous. Other methods are more laborious and much slower. 
     It is envisioned that, via in-situ ultraviolet spectrometry, carbonate ion concentrations can be measured directly at a rate of once per second or faster. In conjunction with in-situ measurement of pH, in-situ visible and ultraviolet spectrometry can be used to rapidly and comprehensively characterize the entire CO 2  system. The principles involved in this analysis can be used for characterization of many kinds of solutions (i.e. a variety of aqueous media), including blood plasma. 
     CONCLUSIONS 
     In the absence of direct spectrophotometric determinations of [CO 3   2− ] T  as described above, [CO 3   2− ] T  must be calculated from measurements of either total dissolved inorganic carbon or total alkalinity combined with either pH or CO 2  fugacity. While spectrophotometric pH measurements are rapid, with acquisition rates on the order of seconds, measurements of dissolved inorganic carbon, total alkalinity and CO 2  fugacity generally require several minutes, as a minimum. Thus, the spectrophotometric procedures for measurements of carbonate ion concentrations described in this work, and those for spectrophotometric pH analysis (Liu et al., 2006), are unique in their suitability for prompt in situ analysis. Spectrophotometric pH and [CO 3   2− ] T  measurement procedures can also be distinguished from those required for A T , C T  and f CO2  with respect to the instrumental simplicity required for the various analyses. In contrast to the procedures and equipment required for analyses of A T , C T  and f CO2 , spectrophotometers are common equipment items in a wide variety of research and teaching laboratories. As has been the case for spectrophotometric measurements of pH, it should be anticipated that the parameters required for quantitative measurements (e.g., equations 21 through 24) will be amenable to further refinement. It should be emphasized in this case that, through measurements of absorbance ratios, future improvements in Pb II  and molar-absorbance-ratio characterizations will allow refinement in [CO 3   2− ] T  measurement accuracy. As long as data are archived as R—S pairs (i.e., absorbance ratio and salinity), measured at 25° C., all data are suitable for quantitative reassessment. As such, observations of Pb II  absorbance ratios provide a molecularly-based index for seawater carbonate ion concentrations. 
     The procedures described in this work are suitable for rapid, quantitative assessments of calcite and aragonite saturation states in seawater. Since the solubility products of calcite and aragonite in S=35 seawater are approximately 10 −6.367  and 10 −6.186  (Millero, 2007), and the total calcium concentration is 0.0103 at salinity 35, the carbonate ion concentrations for saturation with calcite and aragonite are 41.7 μmol/kg and 63.3 μmol/kg, respectively. Comparison of these concentrations with the log  CO3 β 1  results given by equation 11 (log  CO3 β 1 =4.106 at S=35) shows that inorganic Pb II  is partitioned equally between PbCO 3   0  and lead chloride complexes when [CO 3   2− ] T =78.3 μmol/kg. Thus, the procedures described in this work are well suited to measurement of CaCO 3  saturation states both below and well above the saturation levels of calcite and aragonite. 
     It will be seen that the advantages set forth above, and those made apparent from the foregoing description, are efficiently attained and since certain changes may be made in the above construction without departing from the scope of the invention, it is intended that all matters contained in the foregoing description or shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense. 
     It is also to be understood that the following claims are intended to cover all of the generic and specific features of the invention herein described, and all statements of the scope of the invention which, as a matter of language, might be said to fall therebetween. Now that the invention has been described,