Anal. Chem. 1992, 64, 2306-2309
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TECHNICAL NOTES
Determination of Sea Water Alkalinity by Direct Equilibration with Carbon Dioxide J a b A. Breland I1 and Robert H. Byrne. Department of Marine Science, University of South Florida, 140 Seventh Avenue South, St. Petersburg, Florida 33701
INTRODUCTION Shipboard measurements of total alkalinity are very demanding. Currently used procedures invariably involve painstaking measurements of combined titrant-acid and sea water volumes, as well as careful standardization and storage of acids. Most measurement procedures require frequent calibrations of pH electrodes and well-behavedpotentiometric systems in electrically and mechanically noisy environments. We have recently observed that spectrophotometric measurements at sea using double-beamspectrophotometers and multiwavelength measurements provide highly precise and convenient determinations of sea water pH.1-3 Spectrophotometric pH measurements involving observations of absorbance ratios are inherently calibrated, thereby obviating periodic buffer standardizations.* In this work we have combined spectrophotometric pH measurements with sea water pC0z equilibrations for the purpose of demonstrating the precision and remarkable convenienceof COz equilibration methods in determinations of sea water alkalinity. Our reported procedures increase the precision of previous C02 equilibrium alkalinity measurements5 by a factor of 10.
THEORY
[OH- 1 - [H+l +
where KOis the equilibrium constant for Cot gas exchangelo KO = ([COJ
+ [HZCO~I)/PCO,
K, = [HCO; 1tH+I/(tC021+ [H,C031)
(5)
K, = [CO;- 1[H+I/tHCOL 1
(6)
and
Borate alkalinity in eq 1 is calculated as
+WI)
where brackets denote total concentrations of each indicated species and ZIP-] is the sum concentration of all other proton acceptors in sea water including, for example, H3Si04- and HPOr2-. COZgas exchange does not alter the total alkalinity of a solution.9 Exchange of COZwith a sea water sample alters the distribution of species on the right side of eq 1 without altering TA. Equilibration of sea water with a C02 partial pressure on the order of 0.3 atm produces a solution pH on the order of 5.3. In this case, [HCOs-I becomes the dominant alkalinity term in eq 1, accounting for all but approximately0.05 ?6 of the total alkalinity. Through precise measurement of solution pH and pC02, the total alkalinity (1)Byme, Robert H.; Breland, Jabe, A. Deep-sea Res. 1989,36,803810. (2) Clayton, Tonya; Byme, Robert H., manuscript in preparation. (3)Byme, Robert H.Anal. Chem. 1987,59,1479-1481. (4)Byme, R.H.;Robert-Baldo, G. L.; Thompson, S. W.; Chen, C. T. A. Deep-sea Res. 1988,35,1405-1410. (5)Keir, Robin S.;Kounaves, S. P.; Zirino, A. Ana!. Chim. Acta 1977, 91, 181-187. (6)Millero, Frank J. Geochim. Cosmochim. Acta 1979,43,1651-1661. (7)Dickson, Andrew G.Deep-sea Res. 1981,B A , 609-623. (8)Butler, J. N. Carbon Dioxide Equilibria and Their Applications; Addison-Wesley: Reading, MA, 1982. (9)Gieskes, J. M. In The Sea; Goldberg, Edward D., Ed.; Wiley-Interscience: New York, 1974;Vol. 5, Chapter 3.
(7)
where BT,the total boron concentration in sea water, is directly proportional to salinity and KB is defined12as KB = [B(OH): 1tH+I/[B(OH)31
C[P-1 (1)
(4)
and the dissociation constants K1 and KZare defined" as
[B(OH)c I = B&B/(KB
The total alkalinity of sea water (TA) can be described68 in terms of component alkalinity contributions using the equation
TA = [HCO, 3 + 2[C0,2- 1 + [B(OH); 1 +
of the equilibrated sea water sample can be determined by summing the component terms in eq 1. The individual terms in eq 1 are given as follows:
(8)
At pH less than 6 the hydroxide alkalinity, [OH-], is vanishingly small compared to the principal terms in eq 1. The hydrogen ion concentration term, [H+l, is evaluated spectrophotometrically3J3 as pH = - log [H+l = - log IK, + log { ( R- el)/(ez-Re3)) (9) where IKZis the dissociation constant of the sulfonephthalein indicator used in this study, bromocresol purple (BCP): IK, = [I2-][H+I/[HT 1
(10) and the constants el, e,, and e3 in eq 9 are molar absorptivity ratios.3 Spectrophotometric determinations of solution pH with BCP indicator involves absorbance measurements at 589 and 432 nm, the wavelengths of maximum absorbance of the 12- and HI- forms of the indicator. The absorbance ratio, R, in eq 9 is then given as R = M&432A. Measurement of absorbance characteristics of 12- at high pH, and HI- at low pH, provides the following absorbance ratios at 25 "C: (10)Weiss, R. F. Mar. Chem. 1974,2,203-215. (11)Dickson, A. G.;Millero, F. J. Deep-Sea Res. 1987,34,1733-1743. (12)Dickson, A. G. Deep-sea Res. 1990,37,755-766. (13)Breland, Jabe A., Byme, R. H. Deep-sea Res. In press.
0003-2700/92/0384-2308$03.00/0 0 1992 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 64, NO. 19, OCTOBER 1, 1992
2807
g/cm3. Calculation ofg(8) is made utilizing the relationship16 g(8) (cm/s2) = 978.049[1 + 0.0052884 sin' (8) (5.9 X lo4) sin2 (28)] (18)
METHODS Measurement of the bromocresol purple dissociation constant at 25 "C over a range of salinities (S= 29-35.2) yielded the following resultd4 log
= -5.818,
+ (1.29, X 10-3)(S- 35)
(11)
where S is salinity and I& is expressed in mol/kg(,,). Alkalinity contributions from phosphate and silicate can be determined from total phosphate and silicate concentrations in a manner closely analogous to calculation of [I,-], the alkalinity contribution of the bromocresol purple indicator:
[I2-1 = IT*I&/(I&
-t
WI)
(12)
Through our COZequilibration procedures, [ P I is included in the eq 1 summation term, C[PI, and eq 1 is used to determine the equilibrated sample's total alkalinity. This alkalinity is different from the sample's original alkalinity due to an addition of indicator such that IT 20 pM. The relationship between the sea water's initial alkalinity TAi and the sample's final measured alkalinity TAI is
-
TAiVi = T&Vf - ZTVf
(13)
where Vi and Vf are initial and final masses (or volumes) and the term I T v f f O h v 8 from the addition of indicator (alkalinity) as dissolved NazI in pure water. Indicator concentration in the final equilibrated solution, IT,can be directly calculated from measurement of indicator absorbance at the indicator's isobestic point. Since the isobestic point for bromocresol purple is 489.5 nm,14 it follows that
= 489.SA/ (D'M9.5e) (14) where 4 8 9 . 4 is absorbance at 489.5 nm, D is path length (cm) and ~ 9 . 5 6is the indicator's molar absorptivity a t the isobestic point: 489.56 = 7350 cm-1 M-1. Measurement of total alkalinity through COSequilibration procedures requires precise knowledge of the C02 partial pressure. The partial pressure of COZ a t equilibrium is calculated from the relationship IT
(15) where Ap is atmospheric pressure a t the time of equilibration, and XCO, is the C02 mole fraction in the equilbration gas. Sea water vapor pressure, VP(sw), is calculated from the equation (ref 15)
VP(,,, = VP,,,[ 1- O.OOO5364Sl
(16)
where VP(,) is the vapor pressure of pure water a t the equilibration temperature and S is salinity. VP(,)a t 25 "C is 23.756 Torr (760 Torr = 1atm = 101 325 Pa). Atmospheric pressure (AP) can be determined with a mercury barometer, using the following equation:
AP = HOg(8)p,.
(17) where Ho is the height of the mercury column (in cm) corrected to 0 "C,g(O) is the gravitational acceleration a t latitude 8, and PHg4 is the density of mercury a t 0 OC. PHgO equ& 13.5951 (14) Breland, Jebe A. Spectrophotometric determinations of the pH and total alkalinity of sea water utilizing sulfonephthalein indicators. Ph.D.Dissertation,University of South Florida, St. Petersburg, FL, 1992. (15) Riley,J. P.; Chester, R. Marine Chemistry, Academic Press: New York, 1971; Chapter 6.
Sea water samples (S= 35.217) were equilibrated in a round bottom flask attached to a rotary evaporator. The flask, containing 100 mL of sea water (-20 pM in BCP) was partially submerged in a water bath and rotated at 2-4 revolutions per second for approximately 1 h. Our observations indicated that equilibrium was reached in 30-40 min. A refrigerated thermocooler (LaudaModel No. L4K) circulated water (25.0"C) through the condensing coils of the rotary evaporator, through a coiled copper tube in the water bath surrounding the rotating flask, and through a spectrophotometer cell jacket. A small Teflon tube, passing through the thermostated coils of the rotary evaporator, was used to introduce humidified COz gas into the head-space of the reaction flask, just above the gas-liquid interface. The flow of thermally equilibrated, humidified COz was regulated at 50 cm3/minwith a Manostat precision flowmeter (Model No. 36-541-035). The flask head-space was open to the atmosphere at a point -30 cm above the sample. A peristaltic pump (Cole-PalmerModel No. 7520-25)continuously circulated the sample between the rotary evaporator's equilibration flask and a 10-mmin-linespectrophotometer flow cell. The flow rate of circulatingsea water was approximately0.6mL/s. The transfer tubing (3.2-mm4.d. FEP Teflon) plus flow cell volume was approximately 20 mL. Absorbance measurements were made with a Cary 17D spectrophotometer. The temperature was monitored throughout the equilibrations using a calibrated precision thermometer. The basic form of bromocresol purple (I2-) has an absorption maximum at 589 nm and the acidic form (HI-) has a maximum at 432 nm. An additional absorbance reading at 750 nm, where BCP is nonabsorbing, is made in order to adjust for any baseline changes which might occur between the initial blank reading and the final absorbance reading. An absorbance reading at the BCP isobestic point (489.5 nm) is used to calculate IT. For 10mm path lengths and IT 20 pM the relative absorbance contributions of natural dissolved organicsubstancesare generally insignificant, even in coastal waters. Furthermore, if baseline absorbance measurements are obtained using natural samples containingthese absorbingsubstances, this potentialinterference is effectively eliminated. Atmospheric pressure determinations were made using a standard mercury barometer (WelchScientific No. 1215). [Note that for work at sea aneroid digitalbarometers are available which provide a resolution of 10 Pa (0.1 mbar1.1 At the latitude of St. Petersburg, FL (8 = 27" 46'), g(0) in eq 17 was equal to 979.1676 cm/s2. Corrected atmospheric pressure values were periodically compared with those of a local airport (Albert Whitted FAA tower) located less than 1 km from our laboratory. Pressure differences (airport vs laboratory)were never greater than 67 Pa and averaged A19 Pa. Humidification of the equilibration gas was achieved by passing the COz gas mixture through a bubbling frit (pore size C) submerged in several centimeters of deionized water. The gravimetrically determined COz mole fractionof the primary standard C02/Na gas mixture employed in our equilibration experiments (Air Producta and Chemicals, Inc.) was 0.299966.
-
RESULTS AND DISCUSSION The procedure used to calcul~ta(TA)through COn equilibrations is outlined in Table I. The directly measured parameters in our sample calculations are xcq = 0.299 965 f O.OO0 01;H(24.0 "C) = 765.0 mm;R(25O C ) = 0.8500;S = 34.5; ~ . & 2 5 O C ) = 0.1600. Equilibrium data were obtained as follows: ealinity dependence of KO(ref 10); salinity dependence of K1 and KZ(ref 11);salinity dependence of IKZ(eq (16) Press, Frank.; Siever, R. Earth, 4th ed.; W. H. Freeman, New York, 1986; Chapter 19.
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ANALYTICAL CHEMISTRY, VOL. 64, NO. 19, OCTOBER 1, 1992
Table I primary dataa
calculation procedure
derived dataa
eq 16 W,,= 23.32 Torr VP, = 23.756 Torr (25 "C, S = 34.5) H(24 "C) = 765.0 mm correction tables H" = 761.88 m m HO, g(O), PW eq 17 AP = 760.71 Torr = 1.000 94 atm xco*, V p ( S W ) , Ap eq 15 pC02 = 0.291 04 atm S eq 11 log I K = ~ -5.8189 4 8 9 . d eq 14 IT 2.18 X loa M = 2.13 x 10-5 R, S eq 9 pH = 5.2946 PCOZ,PH, KO,K1 eq 2 [HCOs-] = 2.3189 X [co32-i= 5.12 x 10-7 PCOZ,PH, KO,KI, KZ eq 3 S , PH eq 7 [B(OH)r-] = 2.17 X [I2-] = 4.904 X lo4 S, PH, "4 eqs 12 and 14 [HC03-I, [C032-l, eq 1 TAf = 2.3199 X [B(OH)4-1, [I2-], [H+l eq 13 T A ~= 2.3009 x 10-3 Vi = 100 mL, Vf = 100.1 mL, IT
All concentration units in mol/kg(,,
unless otherwise noted.
Table 11. Measurements of Sea Water Alkalinity (S = 35.217,25 "C)Made over a Period of 10 Days
replicate day 1 day 1 day 1 day 3 day 8 day 8 day 10 day 10
pCOd atm 0.290 98 0.290 82 0.290 74 0.290 95 0.291 88 0.291 10 0.291 27 0.291 14
pH"/ (moll kg(,,)) 5.3025 5.3028 5.3030 5.3027 5.3008 5.3024 5.3021 5.3025
average
SD SE
cv
[H+] = [H+lf+ [HS04-I ion concentration."
[HCO3-I/ (mequid kg(,,)) 2.3663 2.3668 2.3674 2.3672 2.3648 2.3667 2.3668 2.3676
(TA)f/ (mequivl kg(nw)) 2.3677 2.3682 2.3689 2.3686 2.3662 2.36805 2.3682 2.3690
(TA)i/ (mequiv/ kg(,,)) 2.34825 2.3487 2.3494 2.3491 2.3467 2.3486 2.3487 2.3495
2.36670 0.00087 0.00031 0.037%
2.36811 0.00089 0.0002~ 0.037%
2.34861 O.OOO89 0.00031 0.038%
+ [HF] where [H+lf= "free" hydrogen
11);salinitydependence ofKB (ref 12). The HIHotemperature dependence is usually given by the barometric instrument manufacturer. Standard barometer-temperature correction tables may also be used (ref 17). The results of eight replicate alkalinity measurements on Gulf of Mexico surface water are shown in Table 11. Our measurements, made over a 10-day period, had a standard deviation equal to 0.89 pequiv/kg(,, and a coefficient of variation smaller that 0.04%. As such, the precision obtained using our procedures is considerably better than that reported by Keir et aL5 The coefficient of variation given by Keir et al.5 on 10 replicate samples was f0.36 7% which, assuming a typical sea water TA of 2.3 mequiv/kg, yields a standard deviation of f8.3 pequiv/kg. The substantially improved precision obtained in the present work is attributed to two factors: (a) improved reproducibility in measurements of pH and (b) improvements in the reproducibility of COz-sea water equilibrations. Our previous work has demonstrated that spectrophotometric pH replicates at sea typically agree to within f0.0005 pH units. Spectrophotometric pH measurements are quite rapid compared to potentiometric measurements and do not require the use of buffer standardizations.lJ8 (17) Dean, J.Lange'sHandbook of Chemistry, llthed.; McGraw-Hik New York. 1973: Chauter 2. (18) Robert-Baldo,-G. L.; Morris, M. J.; Byme, R. H. Anal. Chem. 1985,57, 2564-2567.
The improved reproducibility of COz-sea water equilibrations in our work is principally attributed to elimination of bubbles in our equilibration procedure. Bubble size spectrum and bubble depth can exert a strong influence on effective gas partial pressure. Keir et d5 acknowledgedthat determination of the equilibrium pCO2 effected by their procedures, which involved bubbling through glass frits, was a considerable problem. Our equilibration procedures produced no bubbles yet maintained a well-mixed sample with a large surface area for gas exchange. The accuracy of total alkalinity measurements, using titrametric procedures, is a subject of current concern and controversy. Laboratory intercalibrations1S21have shown that the reproducibility of measurements made by individual laboratories is considerably better than the agreement among laboratories. As a consequence of such studies it haa been recommended that standard reference materials, including alkalinity standards, be prepared and distributed to participants of the global oceanic carbon program. The procedures we recommend for assuring the accuracy of alkalinity measurements at sea are closely tied to the use of standard reference solutions. Since [HCOa-I constitutes approximately 99.95 % of the total alkalinity, TAf,in our equilibrium procedures (Table I), the accuracy of our alkalinity measurements will be very closely related to measurement of this dominant term. Inspection of eqs 2 and 9 shows that bicarbonate alkalinity can be expressed in logarithmic form as follows: log [HCO; ] = log (KS1IIK.J + log $ 0 2
+
log ( ( R- e1)/(e2 -Re3)) (19) the term log (KOK~IIKZ) is comprised of physical-chemical constants, and it is clear that the absolute accuracy of equilibrium alkalinity determinations will be no better that the accuracy of this product of terms. For accurate determinations of [HCOjl, we recommend that assessments of log (KOK~IIK~) be obtained by each investigator in a manner which correlates log pC02 measurements with log (K&/ I&). It follows from our previous discussion that, using a standard reference solution having alkalinity T&, we can write [HCO, l8 = TAB- [I2-1 - 2[C0,2- 1 - [B(OH), 3 + [H'] (20) where [HCOs-I, denotes bicarbonate allralinityof the standard solution at equilibrium. Subsequent to calculation of tHC03-I, using eqs 20 and 1-12, the bicarbonate alkalinity can be described using eq 19, wherein log (KOKIIIKZ) is treated as the only unknown. In this manner the critically important calibration term log (KOKIIIKZ)becomes correlated with each investigator's procedures for determining p C 0 ~ .According to this procedure, the term K & ~ / I Kis~determined as a single entity whereupon any uncertainties in the individual terms KO,K1, and IKZare not cumulative. The method which we used to determine IKZwas very similar to the procedure we have outlined above. The term T& was carefully determined on a sea water sample through acid titrations. Subsequently, through iterative calculations (19) Poisson, A.; Culkin, F.; Ridout, P. Intercomparison of total alkalinity and total inorganic carbon determinations in sea water; UNESCO technical papers in marine science; No. 69, UNESCO: Paris, France, 1990. (20) A Report of the sub-panel on standards for COz measuremente of the Joint Panel On Oceanographic Tables and Standards; UNESCO technical papers in marine science; No. 60, UNESCO Paris, France, 1991. (21) Poisson, A.; Culkin, F.; Ridout, P. Deep-sea Ree. 1990,37,16471650.
ANALYTICAL CHEMISTRY, VOL. 64, NO. 19, OCTOBER 1, 1992
we determined the value of I K which ~ satisfied eqs 2-10 and 12-20. Via this procedure the IKZresults given in eq 11are consistent (correlated) with the product K&1 calculated using the KOresults of WeisslO and the K1 results of Dickson and Millero." Combining our I K results ~ (eq 11) with salinity corrected values for K0l0and K1,ll we obtain the following estimate (25 "C) for the salinity dependenceof the term (K&d IKZ) expressed in mol/kg(,,): log (K&,IIK2) = -1.5740
+ (6.06 X lo4)@ - 35)
(21) Investigations in which we varied temperature at constant salinity and alkalinity demonstrated that log (K&I/IKz) changes by approximately 0.01 unit/OC. Our experiments indicated that, in the event of deviations from 25.0 OC on the order of i 2 "C or less, log (K&~/IK~) can be calculated as
log (K&,I1K2) = 11.1704 - 8458.231T + 13889241P +(6.06 X lo4)@ - 35) (22) where T is absolute temperature (K). Total alkalinity standards can be prepared in sterile sea water, and such standards are expected to become routinely available from Scripps Institution of Oceanography.20 Although future work may demonstrate that measurements of the term K&1/1K2 are sufficiently consistent among various investigators that standard values for this calibration term might be adopted, at the present time we consider the use of alkalinity standards to measure this term at sea as a critically important aspect of equilibrium alkalinity determinations.
2509
The methods which we have outlined are extremely simple in an operationalsense, and we predict that other investigators will find these methods at least as precise and accurate as conventional titrations of sea water using strong acids. It is our expectation that the fundamental simplicity of these equilibration procedures may provide an improvedcoherence in the alkalinity results obtained by a diverse set of investigators. Furthermore, we expect that most investigators will find the use of gas "titrants" a substantial convenience compared to liquids. Although our analyses are principally directed toward investigations of sea water, we expect that these methods should prove useful in monitoring other solutions which have a relatively constant major ion composition. Such systems include physiological fluids, alkaline lakes, geothermal solutions, and a variety of groundwaters. It is important to note, in such cases, that the constant term, K&1IIK2, in eq 19 may be strongly dependent on solution composition. For greatest accuracy, standards should be used which are closely matched to test solutions in their major ion content.
ACKNOWLEDGMENT This work was supported in part by grant number OCE9019629 from the National Science Foundation.
RECEIVED for review January 29, 1992. Accepted June 25, 1992.
