pH, alkalinity and total CO2 in coastal seawater by potentiometric titration with a difference derivative readout

Analytica Chimica Acta 394 (1999) 101±108

pH, alkalinity and total CO2 in coastal seawater by potentiometric titration with a difference derivative readout J. MartõÂn HernaÂndez-AyoÂna,*, Stuart L. Bellib, Alberto Zirinoa,c a

Instituto de Investigaciones OceanoloÂgicas (IIO), Universidad AutoÂnoma de Baja California, km 103, Carr. Tijuana±Ensenada, Ensenada, Baja California, Mexico b Department of Chemistry, Vassar College, Poughkeepsie, NY 12604, USA c Marine Research Division (M.C. 0202), Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093, USA Received 13 August 1998; received in revised form 2 February 1999; accepted 15 February 1999

Abstract A method for measuring three components of the CO2 system, pH, alkalinity (At) and total CO2 (TCO2) in coastal seawater is presented. The measurements are suf®ciently precise to register CO2 changes of biological origin in sur®cial and coastal waters or in culture media. The method is based on a modi®ed potentiometric titration of seawater with acid in a custom-built cell with the data plotted as a difference derivative, giving two peaks from which total carbonate and alkalinity can be computed. pH is calculated directly from the initial millivolt reading of the sample. One important aspect of this technique is that, unlike a Gran titration, the measured values of pH, At and TCO2 are independent of any pre-conceived seawater model. In this work we demonstrate that the relative position of the two peaks (used for determining TCO2) is relatively insensitive to interferences from dissolved organic matter to about 1  10ÿ4 M, while peak height is sensitive to it. This last observation permits the detection of organic bases which might be included in the measurement of alkalinity. # 1999 Elsevier Science B.V. All rights reserved. Keywords: Total CO2; Alkalinity; pH; Organic matter; Coastal zone

1. Introduction In spite of the importance of the carbon dioxide system in buffering pH and as an indicator of photosynthesis and respiration in estuaries, this aspect has received surprisingly little attention [1]. An understanding of the estuarine CO2 system is important to all the branches of marine science. In principle, this *Corresponding author. Fax: +52-6174-5303; e-mail: [email protected]

understanding may be obtained through measurement of any two of the four variables: pH, At, pCO2, and total CO2 (TCO2), and from any of two of these properties the other can be calculated [2]. Traditionally, many data sets have been obtained by the potentiometric Gran titration technique that enables the At and TCO2 to be measured in a single ocean sample. However, this technique is limited by the precision of the constants and by requiring pH electrodes with a nearly perfect Nernstian slope [3]. For example, the results of the transient tracers in the

0003-2670/99/$ ± see front matter # 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 3 - 2 6 7 0 ( 9 9 ) 0 0 2 0 7 - X

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oceans (TTO) North Atlantic expedition showed that the TCO2 determined from Gran titrations was about 20 mmol kgÿ1 higher than that determined by coulometry [3]. This difference was attributed to the presence of unknown protolytes in natural seawater [4]. On the other hand, another study indicated that the offset in TCO2 derived from potentiometric titration relative to direct measurement was (possibly) due to a lack of Nernstian response, not due to unknown protolytes [2]. A further problem with the application of the Gran technique to natural waters is that large errors may be introduced by the presence of other weak acids which make it dif®cult to de®ne the acidimetric titration end point. A sizable fraction of the acid groups on humic substances is titrated in the pH range 4±3 where Gran titrations are normally performed [5]. Clearly, the above will result in analytical imprecision and inaccuracy in coastal water where the composition of organics is unpredictable. In this work, we propose a simple method appropriate for coastal zones that

measures pH, At and TCO2 independently, with high precision. The technique combines a discrete pH measurement method [6] and an acid titration with a potentiometric readout [2,3,7,8]. It uses a specially designed cell which allows both the measurement of pH and titration in a closed system. By plotting the difference derivative, two peaks are obtained which correspond to the protonation of carbonate and bicarbonate ion in solution which are then used to calculate TCO2 and At. 2. Experimental The titration cell is an elongated, water-jacketed container made out of glass (Fig. 1). There is a Te¯on stopcock on one side and on the other side, the cell extends into a large, tapered, threaded, neck. A tapered, hollow `plug' is made to ®t snugly into the neck and can be tightly ®xed to it by a threaded plastic

Fig. 1. Titration cell. (A) Orion (Ross) combination pH electrode, (B) Temperature sensor, (C) Glass burette tip, (D) 2 ml syringe (barrel and plunger), (E) Plastic conduit, (F) Magnetic stirrer, (G) Water-jacketed container.

J.M. HernaÂndez-AyoÂn et al. / Analytica Chimica Acta 394 (1999) 101±108

collar. Through the plug are placed an Orion `Ross' combination pH electrode, a 2 ml syringe (barrel and plunger), a glass burette tip, a sealable plastic conduit for introducing the sample and a thermocouple for sensing temperature. All of the above are sealed into the plug with silicone cement to form a solid stopper. The volume of the system is determined precisely by weighing the cell before and after ®lling with distilled water. The cell volume is approximately 30 ml and its volume was determined to be 0.033% (one standard deviation) by weighing. Approximately 2 ml of acid are used during the titration. The system is closed and the volume of acid added is compensated by displacement of the syringe plunger. In order to prevent mixing of the samples with the atmosphere, samples are obtained with 50 ml syringes. The samples are then introduced into the cell via the conduit, and allowed to ®ll the cell slowly, displacing the air above it, without producing bubbles. The cell is allowed to ®ll and over¯ow. When the volume of water in the syringe approaches the last 5 ml, the cell is tipped upward to allow any bubbles that may have formed to leave the cell via the stopcock. After bubbles have been removed, the cell is then sealed by turning the stopcock, the syringe is removed, and the conduit itself is also sealed (it has a Luer-lock syringe stopcock). The cell is thermostated and the sample temperature is read from the thermocouple output. A magnetic stirrer is used to stir the sample. The pH is calculated from the initial stable potential reading prior to the addition of acid. (Prior storage of the samples in a waterbath ensures that constant temperature and a stable potential are achieved quickly). The pH electrode is calibrated separately in the cell against the standard seawater buffers aminopyridine and trishydroxymethylaminomethane, `tris' [9,10]. The titration commences after the initial mV has been recorded and terminates after the second peak (bicarbonate) has been clearly passed. After a sample has been analyzed, the cell must be rinsed and purged of CO2 adsorbed on the glass walls. This is done by unscrewing the `plug' from the body of the cell, rinsing the cell copiously with distilled water, and then drying the walls with a hand-held, pistol-shaped, hair drier. Two automatic titrators were used in this work. The ®rst was a commercial titrator (Radiometer TT85)

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Fig. 2. Potentiometric titration of CRM Batch 30. Plot of the difference derivative of the electrode response (mV) against volume of HCl in milliliters.

with the electrometer output coupled to a personal computer via the RS-232 port. The second titrator, used presently, consists of a programmable Kloehn precision syringe, a personal computer and a radiometer research-grade pH meter connected to the RS232 port of the computer. The Kloehn syringe is connected to the mouse port. A computer program written in BASIC controls the syringe and reads the electrometer. While the volume of acid added and the `stabilization time' between readings are selectable by the operator, we chose those values which provided good peak de®nition and reproducibility. A 15 ml addition every 10 s was found to give good peaks with the Kloehn pump (Fig. 2). Eighty-seven points were recorded during the 14.5 min. titration. After a titration, the data are processed in a MATLAB program that calculates the difference derivative [11,12], does a spline interpolation, ®lters, and computes peak positions and values. Standard 0.1 M HCl was made up in NaCl to bring the ionic strength to 0.7 M [2]. The acid was calibrated against seawater certi®ed as reference material (CRM) for TCO2 obtained from Dr. Andrew Dickson at the Scripps Institution of Oceanography. 2.1. Model studies In order that the position of the two peaks be analytically useful, it is important to demonstrate that

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Table 1 Constants and conditions used to simulate a titration of seawater with the Complexes formed ÿ

OH HCO3ÿ H2CO3 HSO4ÿ B(OH)ÿ4 HF

EXCEL

program

Conditional constant

Values

Concentration

w 1 2 HSO4 B HF

ÿ13.2174 8.9615 14.8133 1.0240 8.6066 1.0055

Ct ˆ 0.001975 mol/kg of solution Bt ˆ 0.00039 mol/kg of solution St ˆ 0.02957 mol/kg of solution Ft ˆ 0.000065 mol/kg of solution

This model uses the combined Hansson±Mehrbach conditional carbonate constants from ref. [13].

it is not affected by interferences. To explore this possibility, we used two thermodynamic models of ion interactions in seawater to simulate the actual HCl titration. The ®rst, uses the combined Hansson±Mehrbach conditional carbonate constants [13] (Table 1). The second is a more complex (36 species) model of ion interactions which uses individual formation constants at zero ionic strength obtained from the literature and individual ion activity coef®cients [14]. This form was used over other possible seawater representations because it is truly titratable, viz., the constants are completely independent of pH and the model is amenable to the introduction of diverse additional organic (Lewis) bases. Overall, the two models give similar results. Throughout the titration, the individual ion activity model gives pH values within 0.15 pH units of the values produced by the experimentally veri®ed conditional constant model. Model calculations were performed with MICRQL [15] embedded in EXCEL (Microsoft Corporation). 3. Results and discussion Fig. 2 shows the results of a potentiometric titration of the CRM Batch 30, which consists of natural seawater sterilized by a combination of ®ltration, ultraviolet radiation, and an addition of a small amount of mercuric chloride to preserve it. The ®gure shows two clearly distinct peaks, the ®rst of which represents primarily [CO3ÿ]T ‡H‡![HCO3ÿ]T, and the second represents the protonation of bicarbonate species to carbonic acid and CO2(aq), viz, [HCO3ÿ]T‡H‡! H2*CO3. The middle of each peak, as determined by the MATLAB program, is used to determine TCO2 and At (Fig. 2). Although the in¯ection points are obtained empirically, very precise `titrations' of the

seawater model with the conditional constants (Table 1, Fig. 6) show that the equivalents of acid that have combined with Lewis bases to the second in¯ection point are approximately within 2 mmol equal to At as de®ned by [16] and that the difference between the in¯ection points is equivalent to TCO2 within 4 mmol. This is in excellent agreement with the observations of [17] who demonstrated that a small, systematic difference exists between the titration end points (the tops of the peaks) and the stoichiometric carbonate and bicarbonate equivalence points. 4. Precision and accuracy The results of the titrations of six replicates samples of CRM with CRM-standardized acid (another batch with different concentration) are presented in Table 2. The measured error of each component is the total error in the measurement, brought about by the changing of the sample, drying of the cell, introduction of the new sample, etc. The measured precision of pH is 0.0022 pH units, the error in At is 0.18% and the error in the TCO2 measurement is 0.39%, all at one standard deviation (SD). The measured mean value of TCO2 is 1997 mmol/kg, within 8 mmol/kg of the CRM value of 1988.78 mmol/kg. The recommended At value for Batch 30 is 2201.88 mmol/kg. This differences is within 4 mmol/kg of our measured value. The use of CRM to calibrate the acid has certain advantages. First, it avoids errors in standardization of the acid (a major source of variability in a recent intercomparison study, A. Dickson, pers. commun.). Second, it compensates for possible deviations in the electrode slope along the titration curve. Finally, it also compensates for the small difference between the

J.M. HernaÂndez-AyoÂn et al. / Analytica Chimica Acta 394 (1999) 101±108

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Table 2 Results of the titration of five replicates samples of CRM with standardized acid

Table 3 Simulated titrations of the multicomponent model: addition of an organic ligand with a pKa of 9.0

Sample

At (mmol/kg)

TCO2 (mmol/kg)

pH

1 2 3 4 5 6

2201.88 2203.77 2209.45 2201.88 2207.56 2211.35

1986.04 1999.29 2006.87 1999.29 1993.62

7.7442 7.7415 7.7465 7.7432 7.7432 7.7465

Concentration of organic ligand (M)

At (mmol/kg)

TCO2 (mmol/kg)

0.0 1e-5 1e-4 3e-4

2204 2220 2229 2243

1997 1997 1997 1996

Precision Average

0.18% x ˆ 2205.9

0.39% x ˆ 1997.0

S ˆ 0.0022 x ˆ 7.7437

The standard was batch 30 with 1988.78  1.4 mmol/kg total CO2.

end points and the equivalence points. On the other hand, use of the CRM depends on its availability. 5. Model results 5.1. Initial pH As mentioned above, the peaks shown in Fig. 2 are mainly due to carbonate and bicarbonate. Thus, at constant TCO2, the difference between the two peaks is independent of the initial pH. On the other hand the position of the ®rst peak on the x-axis is a function of the initial pH, with the carbonate peak shifting closer to the y-axis with decreasing pH. Hence, there will be fewer titration points to the carbonate in¯ection point. This limits the derivative titration to seawater samples of pH > 7.3 (seawater scale [9]), which is just below the pH of most marine waters. This is not an absolute limitation, since the pH can always be increased by the addition of non-interfering bases (see below). However, this causes additional work and complicates the procedure. 5.2. Organic matter Using the model with conditional constants (Table 1), we tested the effect of the presence of organic matter on the two in¯ection points. Initially, we `added' a hypothetical monoprotic organic ligand with an effective pKa of 9.0 to modeled CRM seawater and measured peak positions. This compound did not increase the difference between the two peaks up to a

Conditions: 2000 mmol/kg TCO2 and pH 7.875.

concentration of 300 mmol/kg (Table 3) and therefore contributed directly to the alkalinity but not to TCO2. The contribution to the alkalinity was not quantitative, however, since the initial pH was only 7.875 and only a portion of the ligand could be titrated. Next, we used the multicomponent model to add a univalent ligand with an acid formation constant of 107.35 to seawater with an initial pH of 8.225 and a TCO2 of 2000 mM/ kg. This is the pKa value of the protolyte thought to be present in seawater by [4] and is close to the pH at which the ®rst in¯ection point occurs. The results of the model titration are shown in Table 4. Within experimental error, the alkalinity value is affected quantitatively while changes in TCO2 are probably not detectable at a loading of 100 mmol/kg base. In conclusion, since natural organic matter is very unlikely to possess an acid formation constant identical to carbonate ion [5,18], it is also very unlikely to interfere in the measurement of TCO2 with this technique. On the other hand, all organic bases in the sample may contribute to At, provided that the initial pH of the sample is suf®ciently high to titrate them. Unlike peak position, peak height and peak shapes are very sensitive to interferences. We tested the sensitivity of peak height to organic matter using the multicomponent model by titrating with mixtures Table 4 Simulated titrations of the multi-component model: addition of an organic ligand with a pKa of 7.35, conditions: 2000 mmol/kg TCO2 and pH 8.225 Concentration of organic ligand (M)

At (mmol/kg)

TCO2 (mmol/kg)

0.0 1e-5 1e-4 3e-4

2397 2405 2498 2702

1995 2000 2005 2019

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Fig. 3. Model determination of the sensitivity of peak height and shape to organic interferences. Additions of a mixture of acetate, malonate, and catechol. Concentrations as indicated in the figure.

of three model organic compounds, `acetate', `malonate' and `catechol' in various proportions, in a humic substance-like matrix. Thus, their effective pKs are about 1 pK unit lower than the respective pure compounds [5]. The results are presented in Figs. 3 and 4. `Acetate' and `malonate' with effective average pKs 3.8 and 4.5, respectively, affect only peak 2 as expected. `Catechol', with effective pK1 of 9.4 and pK2 and 12.6 mostly depresses peak 1. Peak depression and peak broadening of the three compounds is minor below concentrations of 10ÿ5 M (Fig. 4). Above that, it is quasi-linear and relative peak depression becomes a rough indicator of ligand concentration. 5.3. Effect of changes in equilibrium constants We also tested the effect that errors in equilibrium constants may have on peak height. Fig. 5 shows the effect of changing the value of Log KHCO3 in the multicomponent, 36 species model. In the ®gure it can be seen that increasing the value of log KHCOÿ3 from 9.8 to 10.9 dramatically increases the carbonate peak while simultaneously decreasing the bicarbonate peak.

Fig. 4. Peak depression as a result of adding individual "organic matter" to model seawater. (*) Peak 1 (carbonate); (&) Peak 2 (bicarbonate).

In another experiment, and for the purpose of comparison, we have superimposed the titration curve produced with the conditional seawater constants model (Table 1) on the experimental titration curve of the CRM Batch 30. The model curve was adjusted to the same TCO2 content and was made to begin to `titrate' at the same pH value as the actual CRM titration (Fig. 6). Even a cursory scrutiny of the ®gure indicates that the agreement between the two curves is very close (the initial portion of the experimental curve is lost to smoothing). However, there is still a measurable difference between the peak heights of the two curves, especially among the two bicarbonate peaks which may indicate that the conditional constants have not been fully optimized.

J.M. HernaÂndez-AyoÂn et al. / Analytica Chimica Acta 394 (1999) 101±108

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Fig. 5. Result of changing the values of KHCO3 in the multicomponent model.

Fig. 7. Results of the potentiometric titrations of three seawater samples from increasingly within an estuary near Ensenada, B.C., Mexico.

5.4. Field data

within the Bahia de Todos Santos, Baja California, Mexico, while the third is from the bay itself. The pertinent data for the ®gure are shown in Table 5 and demonstrate some of the complexities to be encountered in coastal waters. Fig. 7 shows that the position of the ®rst peak is fairly constant (pH is constant) but that the second peak shifts down®eld as one enters further into the estuary. This effect is principally due to changes in inorganic alkalinity, but the lowering of the peaks as one proceeds into the estuary is probably due to the presence of titratable dissolved organic substances. The shift of the second peak of the `inner water', however, may be beyond the effect of inorganic alkalinity and due to the presence of additional titratable organic matter. Approximate measurements of the total organic carbon content of the samples made with a Beckman TOC analyzer gave values 1, 4

Fig. 7 shows the results of the potentiometric titrations of three seawater samples, two from increasingly within the Estero de Punta Banda which is located

Table 5 Titration data from the three stations in the Estero de Punta Banda, Ensenada, Baja California, Mexico

Fig. 6. Model curve adjusted to the same TCO2 content and same initial pH value as the actual CRM (Batch 30) titration.

Location in estuary

At (mmol/kg)

TCO2 (mmol/kg)

pH

Salinity

Coastal water Middle Inner

2.351 2.406 3.030

2.124 2.169 2.703

8.032 8.008 8.007

33.93 34.22 36.82

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and 7 mg/l, respectively, for coastal, middle, and inner waters. 6. Conclusions The method described here is novel in both cell design and data analysis. The cell design permits the use of relatively small sample volumes and provides a means of measuring the pH independently of At and TCO2 for coastal seawater. Unlike the Gran titration which uses a pre-determined model to extrapolate the titration data in order to calculate non-visible equivalence points, the difference derivative plot provides clear in¯ection points for quantitative analysis. Since the titration provides an additional independent measurement of the carbonate system (pH), it also provides an additional parameter for detecting other (organic) substances, simultaneously titrated with carbonate, if their concentration is suf®ciently high. The technique overcomes two dif®culties through its use of the difference between the carbonate and bicarbonate end points, a possibly low initial pH and high organic content. The ®rst is compensated by a simple pre-neutralization with a non-interfering base. A high content of organic bases, over 1  10ÿ4 M, has been shown to affect only the alkalinity without affecting the calculation of TCO2. The difference between the measured alkalinity and the alkalinity computed from pH and TCO2 provides an additional means of detecting the presence of dissolved, titratable organic components without compromising the carbonate measurements. In studies of the inorganic constituents of seawater, peak heights provide a new tool for detecting interactions among them. Peak heights in conjunction with mathematical models of Lewis acid±base interactions are powerful tools for studying the coastal seawater system.

Acknowledgements We are grateful to Andrew Dickson for his continual support of this project and for making the CRM available to us. This work would not have been possible without his efforts and encouragement. We also wish to thank Angel Del Valls for critically reviewing the manuscript and for many good suggestions. Funding for this project was provided by UABC's Internal Research program. References [1] M. Whitfield, D.R. Turner, The Science of the Total Environment 49(1986) (1986) 235. [2] F.J. Millero, J.-Z. Zhang, K. Lee, M. Douglas Campbell, Mar. Chem. 44 (1993) 153. [3] A.L. Bradshaw, P.G. Brewer, Mar. Chem. 24 (1988) 155. [4] A.L. Bradshaw, P.G. Brewer, Mar. Chem. 23 (1988) 69. [5] M.M. Morel, J.G. Hering, Principles and Applications of Aquatic Chemistry, Wiley, 1993. [6] A. Zirino, Limnol. Oceanog., 20 , 654; Erratum: Limnol. Oceanog, 20 (1975) 698. [7] J.M. Edmond, Deep-sea Res. 17 (1970) 737. [8] I. Hansson, D. Jagner, Anal. Chim. Acta 75 (1973) 363. [9] A.G. Dickson, C. Goyet (Eds.), DOE. Handbook of methods for the analysis of the various parameters of the carbon dioxide system in sea water; version 2. ORNL/CDIAC-74, 1994. [10] F.J. Millero, J.-Z. Zhang, S. Fiol, S. Sotolongo, R.N. Roy, K. Lee, S. Mane, Mar. Chem. 44 (1993) 143. [11] D. Jagner, in: M. Whitfield, D. Jagner (Eds.), Marine Electrochemistry, Wiley, 1981. [12] G. Gran, Anal. Chim. Acta 206 (1988) 111. [13] D.T. Clayton, R.H. Byrne, J.A. Breland, R.A. Feely, F.J. Millero, D.M. Campbell, P.P. Murphy, M.F. Lamb, Deep-sea Res. 42 (1995) 411. [14] S. Belli, A. Zirino, in preparation. [15] J.C. Westall, A. Microql, Chemical Equilibrium Program In Basic, version 2, Department of Chemistry, Oregon State University, Corvallis Oregon 97331, 1986. [16] A.G. Dickson, Mar. Chem. 40 (1992) 49. [17] F. Mclntyre, Mar. Chem. 6 (1978) 187. [18] J. Buffle, Complexation Reactions In Aquatic Systems: An Analytical Approach, Ellis Horwood, 1988.