Spectrophotometric determinations of the pH and total alkalinity of sea water utilizing sulfonephthalein indicators

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Spectrophotometric determinations of the pH and total alkalinity of sea water utilizing sulfonephthalein indicators

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Title:
Spectrophotometric determinations of the pH and total alkalinity of sea water utilizing sulfonephthalein indicators
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Breland, Jabe Armistead
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Tampa, Florida
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University of South Florida
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English
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xiv, 118 leaves : ill. ; 29 cm

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Seawater -- Analysis ( lcsh )
Hydrogen-ion concentration -- Measurement ( lcsh )
Spectrophotometry ( lcsh )
Dissertations, Academic -- Marine Science -- Doctoral -- USF ( FTS )

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Thesis (Ph.D.)--University of South Florida, 1992. Includes bibliographical references (leaves 95-104).

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University of South Florida
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University of South Florida
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028938182 ( ALEPH )
26575943 ( OCLC )
F51-00181 ( USFLDC DOI )
f51.181 ( USFLDC Handle )

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SPECTROPHOTOMETRIC DETERMINATIONS OF THE pH AND TOTAL ALKALINITY OF SEA WATER UTILIZING SULFONEPHTHALEIN INDICATORS by Jabe Armistead Breland II A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Marine Science in the University of South Florida May 1992 Major Professor: Robert H. Byrne, Ph. D.

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Graduate Council University of South Florida St. Petersburg, Florida CERTIFICATE OF APPROVAL Ph.D Dissertation This is to certify that the Ph .D. Dissertation of J abe Armistead Breland II with a major in Marine Science has been approved by the Examining Committee on 18 March 1992 as satisfactory for the dissertation requirement for the Ph.D. degree. Examining Committee: A Ph.D. Member Peter R. BetzeJ01>h D

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Jabe Armistead Breland II All Rights Reserved

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DEDICATION I dedicate this effort to those who have lighted the path so others might follow, and to those who subscribe to the notion that truth is available to those who love it. Of special remembrance are Ethyl Clyde, who encouraged by listening; Hank Baker who taught me to love the sea; and Bob Garrels who helped me to learn from it. 11

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ACKNOWLEIXJEMENTS Standing of the shoulders of others allows one a perspective which is difficult to adequately acknowledge. My current perspective would not have been possible without the help and encouragement of many people. I am especially thankful for the contributions of my committee members. Bob Byrne's insight and resourcefulness are represented m every portion of this dissertation. Without his guidance and encouragement this dissertation would not exist. Peter Betzer also contributed generously to the success of my work. My education would not have reached this point if it wer e not for my parents who gave me faith by having faith. I also thank Jeanne and my children for their forbearance 111

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TABLE OF CONTENTS LIST OF TABLES Vl LIST OF FIGURES Vlll LIST OF SYMBOLS AND ABBREVIATIONS X ABSTRACT Xll INTRODUCTION 1 Historical introduction to oceamc pH and alkalinity determinations 2 Early indicator usage 3 Development of the concept of pH 6 Alkalinity and its measurement from 1900-1940 8 Modern alkalinity methodologies (post 1940) 1 1 CHAPTER 1 HIGH PRECISION MUL TIW A VELENGTH pH DETERMINATIONS IN SEAWATER USING CRESOL RED 1 7 Introduction 1 7 Materials and Methods 1 8 Results and Discussion 1 9 Methodological Considerations 2 9 CHAPTER 2 SPECTROPHOTOMETRIC DETERMINATION OF THE TOTAL ALKALINITY OF SEA WATER USING BROMOCRESOL GREEN Introduction Spectrophotometric pH models IV 35 35 37

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Methods 42 General considerations 4 2 Measurement of molar absorptivity coefficients 4 3 Determination of HF formation constant 1) in sea water Influence of temperature and salinity on spectrophotometric pH calculations Results and Discussion Bromocresol green molar absorptivity ratios Determination of 1 Determination of 1 45 46 47 47 51 55 Sea water titration results 5 5 Calculation of excess hydrogen ion concentrations 6 0 Salinity dependence of 1 T 6 1 Sea water alkalinity determinations 6 8 Precision and accuracy of total alkalinity measurements 7 3 CHAPTER 3 DETERMINATION OF SEA WATER ALKALINITY BY DIRECT EQUILffiRA TION WITH CARBON DIOXIDE 7 7 Introduction 77 Theory 7 8 Methods 8 3 Results and Discussion 8 5 SUMMARY 92 LIST OF REFERENCES 9 5 APPENDICES 1 0 5 1 Techniques for measuring the absorptivity ratios for sulfonephthalein indicators 1 0 6 2 Computations of (T A) from primary data 1 0 9 3 Computer programs for SAS data analysis and data sets for salt and sea water titrations. 115 v

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Table 1 0 Table 1.1 Table 2.1 LIST OF TABLES Page Approximate pH range and color change of the sulphonephthalein indicators. Calculated pH values are shown for replicate sea water samples. Sea water samples were obtained from different Niskin bottles closed at the same depth. It is useful to note that these comparisons are relatively free of inadvertent bias. Since indicator concentrations were generally only consistent within 10%, "replicate" absorbances at each wavelength are distinctly different Consequently, concordant ratios (R=573A/433A) are obtained as welcome surprises. In addition to these comparisons, which suggest that hydrogen ion concentrations in sea water can be measured to 0.10% or better, our examinations of indicator and system stability evidenced no cases of pH dri ft greater than .0008 for periods on the order of 2 hr. Summary of molar absorptivity ratios for bromocresol green at 25 oc. vi 7 30 50

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Table 2.2 Table 2.3. Table 2.4 Table 2.5 Table 2.6 Best fit values from four separate salt solution experiments (25 OC). Comparison of selected values of Fl3t corrected to 25 oc and S = 35. Best fit values for S = 35 sea water at 25 oc [log 1l31 = 4.4166] Comparison of values of s 131 at 25 C in S = 35 sea water. Calculated log Il3t T values at S = 35 and 25C determined using the s 131 results given in Table 2.4. 54 56 57 59 67 Table 2.7 7 2 Replicate measurements on sea water (S = 35.171) using a one step acid addition. Total alkalinity is expressed as meq/kg(sw). Table 3.1 8 6 Table 3.2 Table A.1 Calculation scheme and values calculated from primary data Measurements of sea water alkalinity (8=35.217, 25 oc) made over a period of 10 days. Wavelengths of maximum absorption and extinction coefficient ratios for various indicators Vll 87 108

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Figure 1.1 Figure 1.2 Figure 1.3 LIST OF FIGURES pH vs salinity results are shown for all off-axis stations within our study area (a rectangular area approximately 140 by 200 km). All measurements were obtained at 25 C and 1 atm total pressure. A quadratic fit to our pH vs salinity results is shown for data such that S > 34.50. Our best-fit line is given by pH = 3512.690083 203.769505S + 2 961367281S2. A histogram of residuals, pH(observed) pH(best-fit prediction), is shown for our Figure 1.2 least squares data analysis The vertical axis provides the occurrence frequency (number of calculated residuals) within each residual class On the horizontal axis each residual class is defined in terms of the midpoint 0.00025. As an example, our histogram indicates that 13 residuals were observed at = 0 (-0 00025 < < 0 00025) and 10 residuals were observed at = 0.0005 (0.00025 < < 0.00075). Vlll Page 22 24 26

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Figure 1.4 Figure 2.1 Figure 2.2 Figure 2.3 Figure 2.4 Figure 2.5 On-axis pH observations (o) are added to the offaxis pH observations ( +) shown in Figure 1.2. Absorbance vs. wavelength for the basic (1-2) and acidic (HI-) forms of bromocresol green. Residual Sum of Squares (RSS) vs. log 1 for the Mg/NaCl mixed salt data set. A value of 4.4166 is defined by the minimum residual sum of squares pHT vs log (1 -Q) over the useful indicating range of bromocresol green at S = 35 and t = 25 C. At this salinity and temperature the relationship between pHT and -log(l -Q) can be described by the function log (1 -Q) = 2.5705 I o-(0.95967pHT) log 1 T vs Salinity (at 25 C) obtained from dilutions of sea water with pure water. Linear regression of these 39 points (representing five experiments) yields log 1 T = log 1 T(35) + 0.002577(35 S) ; r2 = 0.967. At 25oc, lo g 1 T(35) = 4.2699. Plot of R(2s)IR(t) vs. temperature R(25 ) is R(t) at 25 oc. R(t) =2A/IA [1A =absorbance at 444nm and 2A= absorbance at 616nm] where 18 o c < t < 32 oc. R(25) can be calculated from R(t) using equation (2.27), [r2 = 0 .989 n= 53], R (25) = R(t) {I+ (0.00907)(t 25)} IX 28 49 53 63 66 70

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LIST OF SYMBOLS BCB = bromocresol blue BCG = bromocresol green BCP = bromocresol purple = [HL-]/[H+][L-2] : first formation constant for the indicator BCG = [HX]/[H+][X] : first formation constant for generalized reaction H++X-=>HX A.Ex = molar absorptivity coeffficient of species X at wavelength A ; defined as; absorbance/(concentration (molar) pathlength (em)). Absorptivity coeffficient ratios: e1 = 6I6EHL /444EHL; ez = 6I6EL /444EHL; e3 = 444EL /444EHL R = absorbance ratio; ie., R = zA/tA (where 2 and 1 refer to AI and A.z. [HD] = concentration of protonated 'dirt acid' [HI] = concentration of protonated indicator M = molar concentration (mol L-1) m = molal concentration (mol kg(waterr 1 ) m a = concentration of acid titrant mH = total hydrogen ion concentration; [in molal units] = [H+]T+ [HI]+ [HD] (H+)T = [H+]T +[HI-] [H+]T = [H+] + [HS04] + [HF] pH= -log [H+] pHT = -log[H+]T pmH = -log { (H+)T + [HD]} Q = { + [H+]1)1 + + [H+]-1)] }I (1+ + FT) X

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XT = total concentration of x[X-] = unprotonated concentration of species x FT = total fluoride concentration [F-] = concentration of unprotonated fluoride ST = total sulfate concentration [S042-] = concentration of unprotonated sulfate ion DT = total dirt acid concentration [D-] = concentration of unprotonated dirt acid S (i) = initial salinity of the sea water sample S (a) = salinity of the acidified sea water sample (TA)s =Total alkalinity (for an exact definition see Dickson, 1981) V s = Mass or volume of sample V a = Mass or volume of acid V sa = Mass or volume of combined sample and acid = microequivalent = micromolal = micromolar nm = nanometers Xl

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water alkalinity. The precision of measurements m the laboratory IS on the order of 1 Jleq/kg. Gas equilibrations are very convenient compared to strong acid titrations. C02 equilibrations obviate demanding volumetric analyses at sea which are requisite to normal titrametric alkalinity determinations. The procedures involved in multiwavelength pH measurements are quite simple relative to the required methodology in single wavelength observations. Abstract approved: Date of Approval Date of Approval XIV Major Professor Robert H. Byrne, Ph D. Professor Department of Marine Science Co Major Professor / Kent A. Fanning, Ph D. Professor Department of Marine Science

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SPECTROPHOTOMETRIC DETERMINATIONS OF THE pH AND TOTAL ALKALINITY OF SEA WATER UTILIZING SULFONEPHTHALEIN INDICA TORS by Jabe Armistead Breland II An Abstract Of a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Marine Scien ce in the University of South Florida May 1992 Major Professor: Robert H. Byrne, Ph.D. Co-Major Professor: Kent A. Fanning, Ph.D. Xll

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Spectrophotometric procedures are presented for determination of sea water total alkalinity over a range of temperatures and salinities. One-step volumetric acid addition with prompt spectrophotometric measurement of excess acid provides total alkalinities precise to 2 microequivalents/kg-sea water. Excess acid concentrations are quantified using the sulfonephthalein indicator, bromocresol green. The procedures for measurement of total hydrogen ion concentration in sea water required determinations of HS04and HF dissociation con s tant s con s istent with the dissociation constant of bromocresol green. The spectrophotometrically derived formation constants in S = 35.00 sea water at 25 C ( = [HS04-] [H+]-1[S042-]-1 = 12.69 molai-1 and = [HF][H+]-1 [F-]-1 = 418 1 molal-1 where [F-] and [S042 ] denote total non-protonated ion concentrations in sea water and [H+] is a free hydrogen ion concentration) are consistent with the assignment log = 4.4166; where = [HI-] I [H+][J -2], and [J-2] refers to the concentration of unprotonated bromocresol green Observations of sulphonephthalein absorbance ratios provide the basis for very precise measurements of sea water pH. An analysis, using cresol red indicates that meaningful pH comparisons at sea can be obtained at the level of 0 001 pH units or better. Comparison s of replicate sea water samples obtained from different Niskin bottles exhibited, in most instances, an agreement within 0.0005 pH units Equilibration with C02(g) and determination of solution pH by spectrophotometry allows precise determination of total sea Xlll

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1 GENERAL INTRODUCI10N Carbon dioxide chemistry is of substantial interest due to the involvement of C02 in a wide variety of biogeochemical processes Interest m C02 chemistry has recently intensified due to the nature of C02 as a 'greenhouse gas' and the central role the ocean plays in the global distribution and transfer of C02. The chemistry of C02 in sea water is generally understood but the questionable analytical precision of a number of C02 system measurements, and the absence of a synoptic view of C02 oceanic distributions make it difficult to disc e rn the o c ean's r e sponse to anthropogenic C02. As a consequence of the increased importance of accurate and precise oceanic C02 system measurements, better analytical techniques to measure C02 in sea water are being sought. It has l ong been recognized that quantitative assessments of C 0 2 m sea water can be obtained through determinations of alkalinity and pH (Johnston, 1916; Greenberg et al., 1933; Rakestraw, 1949; Thompson and Bonnar, 1931; Thompson and Anderson, 1940 ). Early oceanic C02 system determinations were at best semi quantitative due to the difficulty in establishing the solution pH to an accuracy better than 0.02 pH units. Also, as pointed out by Park (1968a,b ), the prevalent use of metal sampling bottles prior to 1955 resulted in sample contamination errors of as much as 0 .04 pH unit and 0 03 meq/L for alkalinity

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2 Understanding of even the conceptual basis for alkalinity measurements apparently came late to the oceanographic community. Rakestraw (1949), discussing the misusages of 'excess base' and 'buffer capacity' in chemical oceanography, was moved to state; "It is proper to seek the cause of this property in what may be called the acid-base balance of the water, but there is a common misapprehension as to what we are talking about, because m chemical oceanography we are still clinging to conceptions which have been abandoned and replaced in the field of general chemistry. Historical introduction to oceanic pH and alkalinity determinations Measurement of acidity can be accomplished through either colorimetric or electrometric techniques Early use of colorimetric and electrometric techniques and the development of the concept of pH are intertwined Advances in both areas led to new models for interpreting acidimetr i c measurements Initially electrodes were not very reliable and the concept of pH was advanced through the use of colorimetry. Although there were recognized shortcomings of colorimetric methods (such as salt effects), corrections for such problems appeared generally satisfactory. With the introduction of more reliable electrodes, higher precision galvanic instruments, and the establishment of standard buffers, beginning in the 1940's electrometric techniques replaced colorimetry as the preferred method for determination of pH. In the section which follows, I have provided a brief review of the use of indicators and the development of the concept of pH. For

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those who are interested several comprehensive reviews can be recommended. A brief introduction to the development of the pH concept is found in Szabadvary (1964a) and an introduction to the use of indicators can be found in Szabadvary (1964b). The early history of indicators is explored in Rancke-Madsen (1972) and a history of titrimetry Is presented by Rancke-Madsen (1958) in "The Development of Titrimetric Analysis till 1806". Early Indicator Usage 3 In the earliest recorded work s indicators were applied to the identification of acid base reactions. The observation that certain indicators (plant juices) changed color through reaction with certain acids and bases was probably made by textile worker s in the sixteenth century or earlier. These observations were of little quantitative significance since the acid-base concept was not fully developed until the late nineteenth century. In fact, one of the earliest and clearest definitions of an 'acid' is that given by the Irish Englishman Robert Boyle (1627-1691) who observed that acids turn plant juices red. The earliest reference to indicator color changes in response to acid-base solutions is that of Iorden (1632) He wrote that one might .... take a piece of scarlet cloth and wet it in Oyle of Tartar and it presently becomes blew: dip it again in Oyle of Vitriol, and it becomes red again." According to Rancke-Madsen (in Bishop, 1972) the first use of an (acid-base) indicator was made by William Lewis ( Lewis, 1767 ) Prior to 1767 indicators were of course known, but interest was

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4 directed mainly at the process and problems of indicator recognition, description and isolation. The indicator presumably used by Lewis was litmus (he made preparations with "infusions of lacmus or blue archil", and is not specific as to which he preferred) which had been affixed to a writing paper and cut into small strips for dipping into solutions to be tested. He employed both sides of the paper, placing the blue form on one side of the paper and the red (acid) form on the other. Lewis was also the first to use standard solutions in acidimetric titrations He was thereby the first to obtain absolute acidities, as opposed to the simple comparative assays then favored because of the apprehension of acidity and alkametry as two separate phenomenon (instead of different degrees of the same phenomenon). Although there was some understanding of indicators prior to the 1660's it is generally recognized that Robert Boyle is responsible for making indicator properties widely known through his "Experimental History of Colors", written in 1664 and widely read In this work he describes various plant extracts capable of color changes (usually red in acid and green or blue in base). Boyle describes the extracts of the plant Heliotropium tricoccum, then called Turnsole, widely used in the dyestuff and paint shops. This extract was also described by DuClos (1671) who employed it as an indicator in investigations of mineral waters Turnsole was later made from extracts of the lichen Lichen rocella and came to be known to chemists as litmus. It is interesting to note here that Robert Boyle is considered the founder of the science now known as chemical oceanography. In

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5 1674 the English chemist and natural philosopher published the first truly definitive scientific paper concerned with the chemical and physical nature of sea water, "Observations and Experiments on the Saltness of the Sea." Boyle was only interested in sea water as a particularly concentrated mineral water and used both evaporation (which he found unsatisfactory) and precipitation with silver nitrate solutions as quantitative tests for determining the amount of salt in sea water (Wallace, 1980). The growth particularly m Germany m the late nineteenth century, of the synthetic organic dyestuff industry produced many new and reasonably pure dyes which found use as indicators. Direct synthesis eliminated one the the major drawbacks in the use of plant extracts, namely the lack of purity of the indicating compound and time required for individual preparations. Stability was also a problem with certain plant extracts. The first successful and usable synthetic (acid-base) indicator was phenolphthalein utilized by E. Luck in 1877 In the same period, other azo-dyestuffs began to be used as indicators. In 1878, G. Lunge introduced methyl orange as an acid-base indicator and by 1893 as many as 14 synthetic indicators were available. Methyl red was introduced in 1908 by E. Rupp and R. Loose. With the introduction of many synthetic indicators the variations in indicator acid-base behavior began to be appreciated. The sulfonephthalein indicators are especially well suited to colorimetric pH measur e ments because as a group they possess a wide range of dissociation constants and sharp, vivid color changes These i ndicators were introduced as a group for pH determinations in

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1915 by H A Lubs and W. M. Clark. The Clark & Lubs color comparitor pH scale became a widely utilized laboratory technique, consisting of various easily fabricated buffers containing the appropriate sulfonephthalein indicator (Clark and Lubs, 1916 & 6 1917; Clark 1928; Snell and Snell, 1948; Tomicek 1951). The sulfonephthalein series with indicating pH ranges are given in Table 1.0. The sulfonephthaleins are diprotic and in Table 1 0 two pH indicating ranges are listed for several indicators. The Clark & Lubs pH colorimeter scale, defined in increments of 0.1 or 0 2 pH units (depending upon the particular indicator) was chiefly employed with special instruments such as the Dubozque comparitor or Nessler tubes, which allowed side by side comparisons of the sample with a set of pH standard buffers containing identical amounts of indicator. Precision on the order of 0 05 pH units was achievable by the careful analyst. The development of the concept of pH Friedenthal ( 1904) was the first to use artificial buffers and a hydrogen ion-color comparison scale (buffer vs sample) to determine the pH of sample solutions. Friendenthal pointed out that only the hydrogen ion concentration, [H+], should be used to characterize solutions, since the alkaline component was always given by 1 0-14f[H+] This essentially constituted the introduction of the pH scale It was useful in simplifying alkaline-acid relationships which heretofore had been separated operationally yet hopelessly entangled theoretically.

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7 Table 1.0 Approximate pH range and color change of the sulfonephthalein indicators Symbol BPB CPR BCP BPR BTB PR CR m-CP 1B XB common chemical name bromophenol blue bromocresol green chlorophenol red bromocresol purple bromophenol red bromothymol blue phenol red cresol red m-cresol purple thymol blue xylenol blue indicator pH range 3.0 4.6 3.8 5.4 4.8 6.4 5.2 6.8 5.2 6.8 6.0 7.6 6.8 8.4 7.2 8.8 1.2 2.8 7.4 9.0 1.2 2.8 8.0 9.6 1.2 2.8 8.0 9.6 color acid base yellow blue yellow blue yellow red yellow -purple yellow red yellow blue yellow red yellow -red red yellow yellow -purple red yellow yellow blue red yellow yellow blue [adapted from Table V .in Tomicek, 1951 and Table 22 in Banyai (1972)]

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8 Alkalinity and its measurement from 1900 to 1940. Early interest in the acid neutralizing capacity of sea water was motivated in large part by a need to understand the limits to which sea water could be subjected (titrated) without affecting its ability to support life. Not many organisms are able to grow and reproduce outside the pH range 4.5-9 Greenberg et al., (1932) suggested that the C02 system would be precisely defined by measuring sea water pH, total C02 and "titratable base". For determinations of total C02, Greenberg et al., 1932 adapted the Van Slyke manometric method for shipboard use. Van Slyke and Neill (1924) introduced a new method utilizing a constant volume appratus in which the final pressure of the liberated gas is measured. The method was good to 1%. The apparatus was easily mounted in a ship's laboratory and took approximately 15 minutes per analysis. Greenberg et al., 1932 discussed the determination of 'titratable base', by noting One of the most readily determined chemical properties of sea water is the amount of base which can be titrated with a strong acid to the turning point of some appropriate indicator Such titrations have long been used but there still remains many disputed points as regards both the methods and the significance of the results". (The term alkalinity was used as early as 1880 by Tornoe to describe the titratable base in sea water, but confusion with [OH-] (also termed alkalinity) and lack of a clear understanding of acid-base relationships in aqueous solution also produced terms such as 'alkaline reserve' and 'buffer capacity' to refer to what we now call alkalinity. Greenberg et al., 1932

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9 preferred the term 'titratable base' to denote "... the quantity of base which can be titrated with a strong acid when the titration is carried to a point at which all the weak acid radicals have been replaced by the acid added." Of course we know now that the indicator chosen will effect the selected endpoint and thus will influence the amount of acid added. In the late 1920 's two methods of determining 'titratable base' were in general use : 1) back titration and 2) direct titration. Both were employed using acid-base colorimetric indicators. In the first instance a strong acid was added to the sample in order to "break up the salts of the weak acids". Then after driving off the C02, the excess acid was backtitrated to the phenolphthalein endpoint. (Tornol, 1880 and Fox, 1909) The first use of the general approach which I employed in section II of this dissertation was described in 1931 by Thompson and Bonnar. Basically the Thompson and Bonnar approach was to determine the excess acid obtained after addition of strong acid to a sea water sample. The amount of excess acid was determined by colorimetric comparisons with a set of standards containing bromophenol blue. These standards were prepared from neutralized sea water (of the appropriate salinity) by adding known quantities of sta ndard acid. A r a nge of pH's could then be determined within the indicating capabilities of bromophenol blue -3 < pH < 4.6 (pK = 3.98, Snell and Snell, 1948) It was recognized that variations in salt content would effect the perceived color s (The 'salt error' of cresol red was investigated by Wells, 1920, and Ramage and Miller, 1925.) Thus standards were to be prepared in sea water having analogous

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salt concentrations. Best results were obtained when the final pH was between 3.7 and 4.4. 10 Mitchell and Rakestraw (1933) applied a one-step acid addition method to (T A) determinations using bromophenol blue. They also employed a chlorinity correction graph which adjusted the apparent pH as a function of chlorinity in order to overcome the salt effect. This provided good agreement in tests performed with sea water and distilled water mixtures down to a chlorinity of -4 g/L. This paper represented a real advance in the use of indicators for quantitative alkalinity assessments. Station data are given for six Atlantic collection sites. Mitchell and Rakestraw suggested that the best accuracy was obtained when the final pH was 3 7 4.0; this being a compromise between the competing factors of poor indicator sensitivity at pH < 3 7 and incomplete titration of the bicarbonate at pH> 4. They give a pK1 = 3.78 for bromocresol blue (BCB) (20 oc and 'high salinity"). The pK1 of BCB was nevertheless taken to be 3.98 (in agreement with the Clark and Lubs pH tube standard) because Mitchell and Rakestraw presumed errors would cancel out when the same pK is used for both standards and samples. In the early 1930's, due to ever improving electronic instrumentation and glass electrodes, potentiometric methods began to replace indicators In a substantial improvement on the method of Thompson and Bonnar (1931), which employed the indicator bromophenol blue, Thompson and Anderson (1940) improved alkalinity methodologies through use of a Leeds and Northrup potentiometer and specially prepared automatic pipets. Their total alkalinity method employed a one-step acid addition method and the

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1 1 resulting pH was determined using a glass electrode standardized against potassium acid phthalate buffer (pH = 4 0). They concluded that use of glass electrodes greatly increased the accuracy of the alkalinity determinations over that obtained utilizing color standards However they also mistakenly concluded that temperature variations and salt effects upon electrode response were not appreciable. Modern alkalinity methodologies (post 1940) West and Robinson (1941) pointed out that variations m (TA) endpoint determinat i ons caused by using different indicators could be reduced if the endpoint was determined potentiometrically. They investigated methyl orange and methyl red (both have very small salt effects on pK Tomice k, 1951) and found their potentiometric endpoint to be intermediate to that of these two indicators. The work of Sverdrup, Johnson and Fleming (1942) indicates that prior to 1940 glass electrodes had not been widely applied to the determination of sea water pH. In their discussion of alkalinity analysis only the early efforts of Ball & Stock 1937 and Buch & Nyna s 1939 are discussed They point out that neutral salts m general, increase the apparent dissociation constant of indicators and therefore give low pH readings Because of the recognized variations in results obtained with various alkalinity methods ( specifically those of Mitchell & Rakestraw, 1933; Gripenberg, 1937; and others summarized in Thompson & Robinson, 1932) Sverdrup, Johnson and Flemming (1942) proceeded to call for a standard m e thod to determine sea water alkalinity Possibly in response to the plea from Sverdrup et al. (1942 )

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12 Anderson and Robinson (1946) developed a rapid electrometric determination of sea water total alkalinity giving a 'probable error' of 1%. This method employed a one step addition of acid to 100 ml of sea water sample. The final hydrogen ion concentration, CH+, was measured with a glass electrode and the procedure was suited to processing large numbers of samples. Conversion of CH+ to pH was accomplished through use of the infamous empirical coefficient, fH+ and the relationship pH = -log (CH+) (fH+) Dyrssen and Sillen (1967) clearly presented Gran function computations required to calculate total alkalinity and total carbonate concentration from emf measurements made during strong acid titration of sea water. Arguments were made for determining and reporting values on a concentration scale which is independent of pressure and temperature (moles per kg of solution). This paper firmly placed potentiometric methods on solid theoretical ground. Refinements in this basic approach are found in more recent works: Dyrssen and Hansson, 1973; Hansson and Jagner, 1973; Bradshaw et al., 1981; Bradshaw and Brewer, 1988b. Culberson et al., (1970) refined the electrometric alkalinity method of Anderson and Robinson (1948), in which pH is determined subsequent to a single step addition of strong acid and removal of C02. Culberson's method required approximately seven minutes per sample and yielded an estimated precision (2 cr) of 0 33% Modem high precision determinations of total alkalinity were considerably advanced with the work of Edmond, 1970. Edmond employed a carefully constructed potentiometric titration cell and Gran plot techniques. Edmond reported total alkalinities at sea with an

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1 3 accuracy (precision) of .17% (95% confidence limit). In the late 1970's a group at the University of Goteborg under the direction of David Dyrssen and L. G. Sillen published several papers on the application of both photometric and potentiometric measurements for determining the total alkalinity of sea water [Dyrssen, 1965; Dyrssen and Sillen, 1976; Graneli and Anfalt, 1977; Anfalt et al., 1976]. Graneli and Anfalt (1977) used bromothymol blue in strong acid titrations and calculated equivalence points using a Gran function and single wavelength absorbance measurements. Various reagents were drawn into a central motorized buret and, subsequent to mixing, absorbance readings were taken with a paired photodiode and light emitting diode. The LED has a peak spectral output centered at 615nm (616nm is the wavelength of maximum absorbance of the basic form of BTB). The time required per titration is approximately 15 minutes. The precision of Graneli and Anfalt's alkalinity determinations was given as .1 %. A similar approach using methyl red as indicator was presented by Anfalt et al. (1976). A submersible probe (containing a light emitting diode and two photodiodes placed at right angles to one another) was used to measure absorbance at 560nm (peak output of the LED). This quasi-double beam instrument operated without ambient light interferences. From six consecutive titrations of the same sea water sample the mean total alkalinity was 1.993 meq/kg 0.007 (0.35% = 1 sigma). Difficulties with the light output of the LED and aging of the diodes were observed at high energy outputs Anfalt et al. also observed problems due to the temperature dependence of the indicator.

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14 Dickson (1981) provided an exact definition of total alkalinity and also refined computations using a non-linear least squares procedure to estimate total alkalinity, (T A), and total inorganic carbon, CT. from titration data Dickson's 1981 work was written m response to the proliferation among marine chemists of various pH scales and the need to select dissociation constants compatible with a given pH scale. Anderson and Wedborg (1983) presented a photometric determination of sea water alkalinity using bromocresol purple. Their instrument was an updated version of the system described by Graneli and Anfalt (1977) with the photodiodes replaced with a colorimeter. They noted that major advantages of the photometric titration were speed and robust construction of the spectrophotometric appratus. My goal in this effort has been to take the basic two wavelength spectrophotometric pH concept, presented by Byrne (1987), and by characterizing the appropriate indicators, fashion methodologies tailored to sea water pH determinations. A natural extension of high precision pH determinations in sea water is to develop alkalinity methods which also utilize spectrophotometric methods. Another of my goals is to provide simple, rapid and highly precise pH and alkalinity methods which can be used at sea with a minimum of error and operator training and which are not dependent upon standard buffer solutions. My investigations identify the precision, utility and simplicity of spectrophotometric pH and total alkalinity determinations in sea water using several indicators. This dissertation is divided into three chapters, which

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1 5 introduce my investigations chronologically. Each chapter develops a single subject and is structured so it could be read (or published) separately. pH precisiOn at sea was first demonstrated on a research cruise in which Dr. Byrne and I both participated. Spectrophotometric analyses of sea water pH using cresol red were performed and results are presented in Chapter One In the laboratory I investigated the behavior of bromocresol green in acidified sea water with the goal of determining its formation constant on the total hydrogen ion concentration scale. Formation constants for bisulfate and hydrogen fluoride were also developed using bromocresol green absorbance measurements in acidified natural sea water The bromocresol green investigations are presented in Chapter Two The precision of a one step acid addition method, with determination of the final pH made solely by determination of bromocresol green absorbance, is also presented in Chapter Two During work on the one step acid addition method I recognized that it was possible to do even better by using COz gas as the titrant instead of a strong acid I present in Chapter Three the results of investigations using bromocresol purple in a gas equilibration alkalinity method which I feel has great promise The gas equilibration technique offers high precision and is so simple I believe it should work quite well at sea. Multiwavelength indicator methods are internally calibrated. New spectrophotometric technologies involving miniature spectrophotometers and fiber optics should further simplify these

PAGE 32

1 6 prectse and accurate approaches to the measurement of pH and total alkalinity. Developments of indicator technology over the past decade presages that much more about the chemistry of the oceans should be revealed by the refined use of this 'old' technology

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1 7 CHAPTER 1 HIGH PRECISION MUL TIW A VELENGTH pH DETERMINATIONS IN SEA WATER USING CRESOL RED Introduction In a senes of prevwus works we have outlined the basis for spectrophotometric determinations of solution pH using both single and multiwavelength analysis (Robert-Baldo et al., 1985; Byrne, 1987; Byrne et al., 1988). Through investigations at sea we have shown that single wavelength measurements can provide pH determinations comparable in precision to shipboard potentiometric determinations (Byrne et al., 1988). Using multiwavelength analyses in the laboratory we have shown that sulfonephthalein indicators provide a molecular basis for assessing solution pH in much the same manner that standard buffer solutions provide a basis for pmsmg solution pH (Byrne 1987). Having expressed, in previous works, our high expectations for the possibilities of at-sea multiwavelength spectrophotometric pH determinations, we report herein the first shipboard investigations of sea water pH using very simple yet highly precise, observations of molecular equilibria. PUBLISHED IN DEEP-SEA RESEARCH, 1989, VOL. 36; 803-810.

PAGE 34

1 8 Materials and Methods A detailed introduction to the principles involved in spectrophotometric determinations of sea water pH can be found m Robert-Baldo et al., (1985) and Byrne (1987). Our shipboard pH measurements were obtained using a Varian Instruments DMS-100 UVVIS spectrophotometer. The sample compartment of this double-beam instrument was thermostated at 25.0 1 C with a Lauda K-4R refrigerated thermocirculator. Other materials required for our measurements consisted of (a) 10cm pathlength absorbance cells with Teflon caps, (b) a 40cm length of tygon tubing for transfer of sea water from Niskin bottles to spectrophotometer cells, (c) a 2 x 10-3 molar solution of the sulfonephthalein indicator cresol red, (d) a 2 mL capacity glass and Teflon Oilmont microburet. Measurements of pH were obtained in four simple steps: (1) Approximately 150-250mL of sea water, drawn directly from a Niskin bottle, were passed through a spectrophotometer cell before the cell was sealed (with no airspace) using Teflon caps. (2) Each cell was warmed to 25.0 C in a thermostated bath. (3) subsequent to drying and cleaning optical surfaces with tissues, each cell was placed in the spectrophotometer sample compartment for measurement of baseline absorbance at 730, 573 and 433 nm. (4) Using a Oilmont microburet, 0.05 0.01mL of cresol red (dissolved in deionized water) was added to each spectrophotometer cell (-30mL total volume). The cell was manually mixed for 20-30s and returned to the spectrophotometer for absorbance measurements at 730, 573 and 433 nm.

PAGE 35

The ratio of cresol red indicator absorbances at 573 and 433 nm was used to calculate sea water pH as follows : 1 9 In the equation above pK2 is a dissociation constant for the reaction HL-(yellow) <==> L2-(red) + H+, R is the ratio of cresol red absorbances at 573 and 433 nm (R = 573A/433A), 1 tL and 2tL are the molar absorptivities of the (1.2) unprotonated (red) form of cresol red at 433 and 573 nm, and 1 f-H L and 2tHL are the molar absorptivities of the yellow (HL-) form of cresol red at 433 and 573 nm. Through laboratory measurements of cresol red and phenol red, we have determined that equation ( 1.1) can be written for sea water (25 C) as: pH=7 .8164+0.004(35-S)+ log { (R-0.00286)/(2.7985-0.09025R)} (1.3) Results and Discussion The principal focus of our spectrophotometric measurements was an assessment of pH anomalies associated with hydrothermal venting (Feely et al., 1987) along the Juan de Fuca Ridge axis. Our measurements using cresol red were obtained over a period of 4 weeks and were confined exclusively to depths between 1000 and

PAGE 36

20 2500 m. In an extended area around the Juan de Fuca Ridge axis below 1000 m it appears that, as a first order effect, pH is controlled be simple mixing of water masses with distinct alkalinity/total C02 characteristics. Due to the relative simplicity of the water mass characteristics below 1000 m in our study area, we are able to reasonably depict our pH measurements as a function of salinity. Our pH measurements obtained using cresol red at off-axis stations (> 1 Okm from the ridge axis; Fig. 1 1) are quite coherent when expressed as a function of salinity In order to quantify the precision of our measurements it is possible to focus on results obtained for salinities greater that 34.5. For salinities greater that 34.5 our pH vs S plot appears to have only very slight curvature. Following the assumption that a perfect measurement system would have provided a perfectly smooth curve, we have fitted (Fig. 1.2) our data for S >34 5 using a quadratic function. Assuming that all deviations from the best-fit line are attributable solely to the imprecision of out pH measurements (e. g. assuming salinity determinations were precise to approximately .0001, and natural deviations from a smooth curve were insignificant), it is possible to assess the upper bound imprecision of our at-sea multiwavelength spectrophotometric pH determinations. Results from 112 data points (Fig. 1.3) indicate that 58% of our measurements were within 0015 pH units of the best-fit line, 84% of our measurements were within .0030 pH units of the best-fit line, and 93% of our measurements were within .0040 pH units of the best-fit line. Our data therefore strongly suggest that spectrophotometric pH measurements have a level of precisiOn such

PAGE 37

Figure 1 1 pH vs salinity results are shown for all off-axis stations within our study area (a rectangular area approximately 140 by 200 km). All measurements were obtained at 25 C and 1 atm total pressure.

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7 550 7.500 J: 7.450 c. 7.400 l 7.350 ........... 34.35 34.40 34.45 34.50 34.55 34.60 34.65 SALINITY 22

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Figure 1.2 A quadratic fit to our pH vs salinity results is shown for data such that 8 > 34.50. Our best-fit line is given by pH = 3512. 690083 203.769505 + 2.961367281.

PAGE 40

24 7.540 7 520 7.500 7.480 7.460 7.440 7.420 7.400 34.50 34.52 34.54 34.56 34.58 34.60 34.62 34.64 SALINITY

PAGE 41

Figure 1.3 A histogram of residuals, pH(observed) pH(best fit prediction). is shown for our Figure 1.2 least-squares data analysis The vertical axis provides the occurrence frequency (number of calculated residuals) within each resudual class On the horizontal axis each residual class is defined in terms of the midpoint 0.00025. As an example, our histogram indicates that 13 residuals were observed at = 0 (-0.00025 < < 0.00025) and 10 residuals were observed at = 0.0005 (0. 00025 < < 0.00075).

PAGE 42

15 14 13 12 11 10 >9 0 s:: 8 C1) ::s 7 C"' C1) 1.. 6 u. 5 4 3 2 1 0 'O:t'O:tMMNN.-.- I I I I I I I I d pH 26

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Figure 1.4 On-axis pH observations (o) are added to the off-axis pH observations ( +) shown in Figure 1.2.

PAGE 44

28 7.540 7.520 7.500 7.480 7.460 7.440 7.420 7 .400 34.50 34.52 34.54 34.56 34.58 34.60 34.62 34.64 SALINITY

PAGE 45

29 that natural variations on the order of .004, and perhaps smaller, can be clearly resolved. Further evidence for this perception is seen in the axis data (stations directly over the Juan de Fuca Ridge; Fig. 1.4). For deep water stations (S>34.6) acidification of water samples, attributable to vent effluents, is clearly visible Although the anomalies due to venting are quite prominent, the magnitudes of the anomalies are generally less than 0 .01 pH units (Fig. 1.4). Salinity measurement imprecision on the order of even .00 1 units will induce apparent imprecision in our pH vs S plots on the order of .001 pH units. It is possible that the pH imprecision depicted in Fig. 1 3 is attributable to a confluence of factors, among which the actual spectrophotometric measurement process contributes only a minor part. Support for this contention is provided in Table 1.1 which shows only one set of duplicate readings with a difference greater than 0.0006 of a pH unit. These comparisons suggest that, if instruments capable of resolving absorbance differences on the order of 0 0001 absorbance units were taken to sea (rather than the 0.001 resolution in s truments used in the present study), meaningful sea water pH comparisons might be made near the level of 0.0001 pH units. Methodological recommendations The concentrations of cresol red used in our determinations were sufficient to provide absorbances at 433 and 573 nm on the order of 0.4-0.8. Unle s s a very high quality instrument is used, it is generally inadvisable to obtain absorbances much larger than 1 0.

PAGE 46

30 Table 1.1 Calculated pH values are shown for replicate sea water samples. Sea water samples were obtained from different Niskin bottles closed at the same depth. It is useful to note that these comparisons are relatively free of inadvertent bias. Since indicator concentrations were generally only consistent within 10%, "replicate" absorbances at each wavelength are distinctly different. Consequently, concordant ratios (R=573A/433A) are obtained as welcome surprises. In addition to these comparisons, which suggest that hydrogen ion concentrations m sea water can be measured to 0.10% or better, our examinations of indicator and system stability evidenced no cases of pH drift greater than .0008 for periods on the order of 2 hr. Salinity Ratio pH Average Range 34.529 1.1027 7.4284 7.4295 5 0.0023 1.1083 7.4307 34.616 1.3345 7 5145 7.5143 0 0.0004 1.3333 7.5141 34.613 1.3209 7 .5099 7 .5100 5 0.0003 1.3220 7.5102 34.520 1.0860 7.4216 7.4213o 0.0006 1.0847 7.4210 34.378 0.9732 7.3727 7.3729 0 0.0004 0.9739 7.3731 34.050 1.0225 7.3963 7.3960o 0.0006 1.0211 7.3957 34.482 1.0376 7.4012 7.40llo 0.0002 1.037 3 7.4010 34.597 1.2806 7.4958 7.4956s 0.0003 1 .2797 7.4955 34 .593 1.251 2 7.4853 7 .4852g 0.0004 1 .2507 7.4851 1.2516 7.4855 1.2508 7.4852

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3 1 Indicator absorbance determinations are obtained as conjugate measurements in the presence and absence of indicator In addition to measurements at wavelengths where indicator forms are strongly absorbing, we strongly recommend that additional measurements are obtained at wavelengths where indicator absorbance is negligible At 730 nm cresol red is nonabsorbing and conjugate measurements with and without indicator should, ideally, be identical. Consequently absorbances at 730 nm can be used to correct for small baseline shifts dominantly attributable to light scattering Subsequent to the addition of indicator to sea water we obtained absorbances at 730 nm occasionally as much as 0.005 absorbance units higher or lower than the baseline reading at 730 nm. In essentially every case these perturbations were found to be due to physical interferences in the optical path. Upon removing interfering particles, bubbles and other imperfections from the optical path (through agitation of the solution and/or cleaning of optical windows) absorbance readings were generally within 001 and with few exceptions, were with i n .002 units of the baseline absorbance. We endeavored to reduce 730 nm absorbance differences to the lowest level possible Baseline studies demonstrated that absorbance deviations at 730 nm closely mimicked the magnitude and sign of deviations at 573 and 433 nm. Consequently absorbance deviations at 730 nm should be subtr a cted (when positive) from absorbances at 573 and 433 nm, and added when negative. As an example, if an absorbance reading at 730nm became +0.001 subsequent to adding indicator to sea water then 0.001 should be subtracted from the indicator absorbance measurements at both 573 and 433 nm.

PAGE 48

32 Our wavelength choices 573 and 433 nm, are identical to the molar absorptivity maxima of the L2(red) and HL(yellow) forms of cresol red. There are a number of reasons for our selection of these wavelengths ( 1) Sensitivity of the absorbance ratio (R) to pH is maximized when R = 573A/433A. (2) Indicator absorptivities change with temperature. Absorbance peaks narrow with decreasing temperature such that the molar absorptivities at each peak increase, and on the shoulder of each peak molar absorptivities decrease By selecting the wavelengths 573 and 433, wavelengths corresponding to the L2and HLmolar absorptivity maxima, similarities in the temperature dependence of 2tL and 1 tHL dampen the influence of temperature on R. (3) The absorbance maxima of each indicator form are sufficiently broad that even for instruments having spectral band widths between 1 and 2 nm, indicator absorbances at 573 and 433 nm will not be distorted by instrumental averaging. ( 4) The wavelengths of maximum absorbance for both L2and HLcan be easily and unambiguously verified in the event of wavelength calibration uncertainties. Fortunately, measurements of cresol red absorbance ratios at 573 and 433 nm are quite insensitive to inadvertent temperature excursions This condition is due in part to similarities in the dependence of 573tL and 433tHL on temperature, but appears to be dominantly attributable to the very similar temperature dependence of sea water pH and sulfonephthalein pK2 (equation 2). Variation in sulfonephthalein pK2 with temperature (Robert-Baldo et al., 1985) is very similar to the ...... Q.Ol/C change in sea water pH As a result, R = 573A/ 43 3A readings are remarkably insensitive to temperature

PAGE 49

33 variations Even after deliberately warming of cells, induced by operator handling, we observed that changes in R through time upon placing cells in the thermostated compartment were generally difficult to detect. Toward the goal of providing pH accuracy on the order of the precision reported in this work, revisions (hopefully small) in our reported molar absorptivity ratios and pK2 behavior may in time prove necessary. Until such time that a concensus set of parameters (pK2, 2tLit tHL, etc .) is developed for sea water pH measurements, it will be especially useful to compile spectrophotometric pH results m the form: indicator type, absorbance ratio, salinity, temperature Should pK2 and molar absorptivity measurements undergo future improvements data in the form (R, S, T) for a given ind i cator will provide increasingly accurate pH assessments, with undiminished precision. As a final point, it is desirable that the c ompositions of indicator solutions should be reasonably well defined. It is not important that the absolute concentrat i on of indicator be known to better than about 10% unless one is pursuing precision better than 001 pH units. We do recommend, however that the pH of the indicator solution be adjusted if necessary to the approximate condition pK2-0.3 < pH < pK2. This can be a c complished satisfactorily by adding acid or base to the indicator (dissolved in deionized H20) while measuring pH on the NBS scale using 7.413 phosphate buffer. The pH of the indicator solution should be complied along with pH data in the form (R, S T) in order that each seawater-indicator mixture has a well-defined composition. As an alternative to the use

PAGE 50

34 of electrodes in the titrant characterizations, it is possible to simply measure the R = 573A/ 433A value of the primary titrant solution subsequent to the titrant's partial neutralization In our experiments, the ratio 573A/433A in our cresol red titrant solution, measured with a 0 10 mm pathlength cell, was found to be 1.42. We feel that the use of indicator methods for pH measurements m seawater has much promise Measurements of absorbance ratios us i ng sulfonephthaleins in seawater can be remarkably precise and, we suspect that if uniform protocols are adopted measurements by independent investigators, will prove highly reproducible

PAGE 51

CHAPTER 2 SPECTROPHOTOMETRIC DETERMINATION OF THE TOTAL ALKALINITY OF SEA WATER USING BROMOCRESOL GREEN In trod ucti on 35 Sea water alkalinity determinations are routinely performed by monitoring the pH of solutions titrated with strong acid. Favored analytical methodologies have included (a) single-step acid addition with potentiometric determination of excess acid (Culberson et al., 1970), and (b) multi-step acid addition with non-linear analysis of the buffer intensity vs pH functionality (Edmond, 1970; Bradshaw et al., 1981; Dickson, 1981). Multi-step methods have been of special use to marine chemists since non-linear analysis of multi-point titrations provides estimates of not only total alkalinity but also total carbon dioxide. The importance of this feature of the multi-step method has been considerably diminished by the advent of highly precise coulometric methods (Johnson et al., 1985) for total C02. In consideration of this development it should be noted that, toward the sole objective of total alkalinity determinations single-step titrations are rapid and conceptually simple relative to multi-point titrations.

PAGE 52

Alkalinity determinations involving single-step acid additions and elimination of C02 from samples (Culberson et al., 1970) do not require quantitative characterizations of weak acid dissociation constants. 36 In the present work we have sought to improve upon the single-step alkalinity procedure of Culberson et al. ( 1970) by combining the speed and conceptual simplicity of the single-step addition method with the convenience and precision of spectrophotometric pH determinations. According to the procedures outlined below, sea water alkalinity is determined by ( 1) acidifying sea water with a strong acid, (2) purging the acidified sea water sample of its C02 with a stream of N2 and (3) spectrophotometrically determining the excess acid concentration in the purged sample. Total alkalinity is determined by using the following equation: (TA)s Vs-Ma Va =(H+)r Vsa (2.1) where (TA)s is total alkalinity of the sea water sample, Ma is the concentration of the hydrochloric acid added to the sea water sample and (H+)r is the total excess hydrogen ion concent r ation in sea water sample which has been completely purged of C02. The symbols V s, V a and V sa are the volumes (or masses) of the initial sea water sample, added acid, and combined sea water plus acid. In employing equation ( 1) for alkalinity determinations it is relatively easy to obtain accurate measurements of V s. Va, V sa and Ma. However measurement of the excess hydrogen ion concentration, (H+)T is a comparatively demanding task. Potentiometer based measurements of (H+ )T require painstaking care of electrodes and accurate electrode calibration In the present work we describe relatively convenient

PAGE 53

37 procedures for spectrophotometric determination of excess hydrogen ion concentrations, (H+)T. The procedures which are described in this work involve the use of a sulfonephthalein indicator, bromocresol green, which has a useful pH indicating range between 4.6 and approximately 3.4. Excess hydrogen ion concentrations within this range of pH can be expressed as a function of the absorbances of the indicator at two wavelengths. Our procedures for expressing total hydrogen concentrations in terms of bromocresol green absorbance characteristics involve the following analyses which are described m some detail later m this paper: (1) measurement of the relative molar absorbance characteristics of protonated and unprotonated forms of bromocresol green; (2) characterization of formation constants appropriate to BCG protonation equilibria in synthetic salt solutions and sea water; (3) spectrophotometric determination of the HS04formation constant in sea water; ( 4) spectrophotometric determination of the HF formation constant m sea water. In addition to our development of a working spectrophotometric procedure for sea water alkalinity determination, our observations permit us to comment on the existence of an 'unknown protolyte' (Bradshaw and Brewer, 1988a) in sea water. Spectrophotometric pH Models Spectrophotometric pH measurements involving

PAGE 54

38 sulfonephthalein indicators are based upon observations of the r"elative concentrations of protonated (H2I, HI-) and unprotonated (1-2) forms of each indicator. Since the relative concentrations of I-2 and HIare controlled by the equilibrium I-2 + H+ <---> m, (2.2) the relationship between the concentrations, denoted as brackets [ ] of H+, HIand I-2 can be expressed in terms of formation constants, such that = [ID-] [H+]-1 [I-2]-1 (2 3) and pH= -log [H+] =log +log {[I-2]/[HI-]} (2.4) The indicator which we have chosen fo r use in single-step sea water alkalinity determinations, bromocresol green or BCG, has a useful indicating range near pH 4. For BCG the absorbance characteristics of I-2 and HIare such that a pure solution of I-2 appears blue and has an absorbance maximum at 616 nanometers, while HIappears yellow and has an absorbance maximum at 444 nm. A mixture of the two forms in approximately a one to one ratio appears green. For solution pH greater than approximately 3, absorbance contributions from the H2I form are negligible. If absorbance measurements are made at two wavelengths (A 1 = wavelength 1 and A2 = wavelength 2), with the wavelengths of maximum absorbance for each form being particularly good choices, it can be shown (Byrne, 1987) that equation (2.4) can be written as

PAGE 55

pH= log + log {(R-e1)l(e2-Re3)} (2 .5) where, e1 = 2EH1 I 1EH1, e2 = 2E1 I 1EH1 and e3 = 1 I 1EH1 represent ratios of molar absorptivity coefficients, A.Ex for each 39 indicator form, x, at a specified wavelength A. ; pH = -log [H+] [H+] = free hydrogen ion concentration; and R is the ratio of absorbances (R = 2AI 1 A) at wavelengths 2 and 1. Sea water which has been purged of C02 will have a total alkalinity very nearly equal to zero at a solution pH near 6.1. If such a solution is titrated with a strong acid, the total concentration of acid added to the solution can be expressed as the sum of the free hydrogen ion concentration, [H+], and the concentration of acid which becomes associated with various sea water anions at pH < 6.1 Terms such as [HS04-] and [HF] contribute significantly to the total hydrogen ion concentration in sea water. If a sea water contains BCG, it is also necessary to consider the contribution of HIto the total hydrogen ion concentration. In addition, since uncharacterized weak acids have been reported both in synthetic solutions (Ciavatta, 1962; Bradshaw and Brewer, 1988b) and sea water (Bradshaw and Brewer, 1988a), we consider, in our work, contributions of such acids to the total hydrogen ion concentration in acidified sea water. The total hydrogen ion concentration in our sea water solutions (purged of C02) is defined as mH = [H+] + [HS04-] + [HF] + [HI-] + [HD] (2 6)

PAGE 56

40 where [HD] is the concentration of any unknown protolyte in our solutions The concentrations of the four acids on the right side of equation (6) can be expressed in terms of formation constants, xl3t for each acid, HX, and the concentration of free hydrogen ions in solution; thus if we write, [HX] = xJ31 [X] [H+], (2.7) equation (2.6) can then be written m summation notation as 4 mH = [H+] (1 + L xJ31 [X]). X=1 (2.8) The total concentration of each protolyte can be written m general form as XT =[X]+ [HX] Equations (2.8) and (2. 9) can then be combined to yield 4 mH = [H+] ( 1 + L xJ31 (XT -[HX])). x=1 Combining equations (2 7) and (2 9) we obtain [HX] = xJ3I XT ( xJ31 + [H+]-1)-1 combining equations (2 1 0) and (2.11) we obtain 4 (2.9) (2.10) (2.11) mH = [H+] (1 + { xJ31 XTxJ312 XT (xJ31 + [H+]-1)-1} ) (2 12) Defining pmH as follows,

PAGE 57

41 pmH = -log mH, (2.13) and combining equations (2 5), (2 12) and (2. 13) yields the general result, pmH = log +log { (R-e1)/(e2-Re3)} -4 log (1 + { XTXT + [H+]-1)-1}) (2.14) where [H+] 1 is calculated usmg equation (2. 5). For sea water our model equation (2 14) can be written explicitly as pmH =pH-log { 1 + + FT + + DT + [H+]-1) + [H+]-1) + [H+]-1) [H+] 1)} where pH is defined in equation (2 5) and [H+]-1 = 10 PH. (2.15) The symbols ST FT, h, and DT in equation (2 15) correspond to the generalized symbol X T in equation (2.14) and denote the total concentrations of sulfate, fluoride, bromocresol green and "unknown protolyte" (dirt acid, Sillen, 1971) -in our sea water samples. The symbols correspond to in equation (2.7), and denote the protonation (formation) constants of HS04-, HF, HI-, and HD. The immediate goal of the research described in this work was the experimental determination of molar absorptivity ratios, ei and formation constants (x 1) for each of the parameters shown in

PAGE 58

42 equation (2 15). The ultimate goal of our work was the development of a convenient spectrophotometric procedure allowing determination of total excess acid concentration m acidified sea water. A portion of our work involved the use of synthetic solutions. Equation (2.15) was also used to describe pmH as a function of R in our synthetic media. However, in our synthetic media, it was possible to truncate equation (2.15) by noting that ST = 0 and FT = 0. Methods General considerations Absorbance measurements were made with a Cary 17D spectrophotometer. All titrations were performed within a 100 mm pathlength open top quartz cell placed in the sample compartment of the spectrophotometer. The cell was fitted with a plastic top having openings for a stirring rod, gas purge tube, combination electrode, thermometer and teflon syringe needles The sample chamber lid permitted continuous stirring and gas purging during absorbance measurements. Cell compartment temperatures were maintained to within + 0.1 degree Celcius (C) with a Lauda K4R thermocirculator. Direct checks of the solution temperature were made with a calibrated thermometer. For each acid titration, 100 or 150 mL of nitrogen purged solution was pipetted into the titration cell. Subsequent to the baseline determinations, bromocresol green (BCG) stock solution (2 x 10-3 m) was added, making final solutions approximately 2-3 J..Lm m BCG. The solution was stirred and titrated (with 0.100 M HCl, in

PAGE 59

43 increments of 0.01 mL) between an initial pH of approximately 6 1 and final pH of approximately 3. Absorbances read to the nearest 0.0001 absorbance unit were recorded at 444, 616, and 750 nm, for each titration point. Additions of 0.100 M HCl were made with a Gilmont ultramicroburet (model S3200 calibrated to 0.001 mL) fitted with a flexible teflon syringe needle. All other titrants were added with a Gilmont microburet (model Sl200, calibrated to 0.002 mL) fitted with a teflon needle In order to adjust the initial sea water pH to a point where there is minimal alkalinity (pH 6.1 ), a Ross combination electrode (Orion model #810200) was used for semi-quantitative pH measurements in the range 5.6 6.6. The electrode was calibrated with NBS phthalate buffer. Solutions were prepared with doubly deionized water and reagent grade salts obtained from J .T. Baker or Mallincrodt. Measurement of molar absorptivity coefficients Determination of bromocresol green molar absorptivities, A.tx were obtained in 0 .71m NaCl, 0.71m KCl and S=35 sea water Our measurements were conducted using 2-3 micromolar BCG indicator concentrati ons, providing maximum absorbances ( 1 OOmm pathlength) at 616 nm on the order of 0 9 and maximum absorbance at 444 on the order of 0.4. 1 M NaOH was initially added to raise the pH to between 8 and 9 After absorbance readings were taken at 444, 616 and 750 nm, the pH was lowered to approximately 2 usmg 1 M HCl and absorbance readings were again recorded at each wavelength Examination of our data for possible baseline shifts

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44 were made by monitoring absorbances at 750nm where BCG is non absorbing Individual molar absorptivity coefficients (tEHI, 2Em, 1, and 2) were used to calculate molar absorptivity ratios (et, e2, and e3). Molar absorptivity coefficients obtained at pH 2 were iteratively corrected for the presence of small concentrations of I-2 (at pH 2, [I-2]/[HI-] 0.004). Determination of 1 and 1 Titrations of simple salt solutions which contained BCG were used to create data sets in the form of paired pmH and absorbance ratio R= 6t6A/ 444A, observations. Our independent variable was measured directly as the ratio of absorbances at 616 and 444nm. The dependent variable pmH was directly calculated as pmH = -log mH where mH is the concentration of H+ in solution, in all forms. The value of mH defined in this manner can be obtained directly from volumetric considerations. Our simple-salt-solution titration data were analyzed using the following equation, pmH= log + log { (R-el)/(e2-Re3)} -log { 1 + 1P1IT + DT [H+]-1) + [H+]-1)} (2 16) A non-linear least squares analysis, Marquardt algorithm (SAS 1984), minimized the residual sum of squares function RSS = L { pmH(observed)i pmH(predicted) i } 2 through the following procedure: An initial least squares fit with IT = 0 and DT = 0 provides an initial estimate for log In a following least squares analysis [H+]-1 is

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45 calculated using equation (2.5) and the initial log IJ3I estimate In a series of successive refinements, involving equations (2.5) and (2.16) an internally consistent set of parameters is obtained which minimizes the residual sum of squares for a given titration. Our sea water titration data (pmH(observed) R) were analyzed using equations (2.5) and (2.15). In analysis of our sea water titration data, which were conducted at S = 35, log IJ3I was assumed to be identical to the best fit log IJ3I value obtained using a simple NaCl/MgCb synthetic sea water (0 528m NaCl and 0.060m MgCh) With this assumed value for log IJ3I in sea water, and a value for log FJ3I obtained in a separate set of measurements described below, our sea water titration data were used to obtain estimates for log s J3I log oJ3I and DT. Determination of HF formation constant (FJ3I) in sea water The formation constant of HF in sea water was determined using procedures similar to those employed by Byrne and Kester ( 197 4) in examinations of boric acid dissociation in sea water. Titrant solutions containing HF and Fin known ratios were prepared in 0 71m NaCl. The addition of our F-!HF mixtures to sea water caused the sea water's pH to approach the value pH = log FJ3I + log [F]/[HF] (2.17) where [F]/[HF] is the ratio of Fand HF concentrations m our titrant. The pH of the sea water used in our experiments was determined using equation (2.5) and the log IJ3I value determined in a synthetic

PAGE 62

46 sea water having the same Mg2+JNa+ molar ratio as natural sea water and a formal ionic strength equal to 0.71m. The [F-]J[HF] ratio in one of our titrant solutions was [F-]/[HF] = 3.016 0.005. As such, addition of F/HF titrant to our sea water solution caused the pH to approach the value; pH = log 1 + 0.4794. Through a series of experiments we found that addition of titrant caused no pH change when pH = 3.097. Addition of titrant at lower pH caused the pH to increase, and addition of titrant to sea water having an initial pH greater than 3 097 caused the sea water pH to decrease. Influence of temperature and salinity on spectrophotometric pH calculations Temperature influences spectrophotometric pH measurements through the influence of temperature on both 1 and sulfonephthalein molar absorptivities. Rather than attempt to resolve these influences on 1. we examined the net influence of temperature on the absorbance ratio, R = 616AI 444A. As such, we attempted to answer the following question: If a set of absorbance measurements are inadvertently conducted at a temperature other than 25.0 C, how can the ratio at standard conditions (25.0 C) be calculated? Our examinations of the influence of temperature on BCG absorbance ratios were conducted using sea water (pH=4) which had been purged of C02. As the sea water was continually bubbled with nitrogen, temperature was varied between 19 and 31 C. At the end of each of four experiments the temperature was returned to 25.0 C. In each case the initial and final absorbance ratios were identical, indicating that no irreversible changes had occurred during the

PAGE 63

47 procedure. Our examinations of the influence of salinity on spectrophotometric pH calculations were conducted using sea water purged of C02. The initial pH of two experiments was pH 4 .1. Three additional experiments were performed at an initial pH of 3 7, 3.6 and 3.4. The initial hydrogen ion concentration in our experiments was calculated from absorbance ratio observations and equilibrium data appropriate to S = 35 and t = 25.0 C. Our solutions were titrated with deionized water, and hydrogen ion concentrations were calculated from the measured dilutions of our initial sample. Through paired observations of hydrogen ion concentration and the term log {(R ei)/(e2Re3)} the equilibrium characteristics of BCG in sea water were examined as a function of salinity. Results and Discussion Bromocresol green molar absorptivity ratios Absorbance as a function of wavelength for the bromocresol green forms I-2 and HIare shown in Figure 2.1. The bromocresol green molar absorptivity ratios (e1, e2, and e3) obtained m this work are given in Table 2.1. The molar absorptivity results shown in Table 2 1 indicate that, at constant temperature, molar absorptivity ratios are insensitive to medium composition. Consequently the average results (e1 = 0 0013}, e2 = 2.314g, and e3 = 0.1299) were employed in equations (2.5, 2.14, 2.22, etc.) for subsequent descriptions of solution pH.

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Figure 2.1 Absorbance vs. wavelength for the basic (1-2) and acidic (HI-) forms of bromocresol green (BCG).

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(\j' d E ..... 0 () al 0 ...:. E ..... 0 -o u <( ,... co ll) ("') c:i c:i c:i c:i c:i aoueqJosqy N .,... c:i c:i 0 ll) ,... 0 0 ,... 0 ll) co 0 0 co 0 ll) ll) 0 0 ll) 0 ll) 0 0 c:i 49 ,........ E c: ...... .c: C) c: Cl) Cl) > cu 3:

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. Table 2.1 Summary of molar absorptivity ratios for bromocresol green at 25 oc. Absorptivity 6t6HI/444HI Ratio Media 0.71m NaCl 0.71m KCl sea water s = 35 Average +1 Std. dev. -0.00042 0.00044 0.00243 0.00182 0.00228 0.00131 0.0012 2.31878 2.34035 2.29216 2.31783 2.31799 2.314s 0.017 0.12750 0.13141 0.12975 0.12891 0.13261 0.1299 0.002 50 Molar absorptivity coefficients, A.x, (x= HI or I) are defined as; Absorbance( at A.) I [total dye concentration(molar)pathlength(in em)]

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51 Determination of 1 The least-square minimization procedure for log 1 determination in a simple salt solution is illustrated in Figure 2.2. The log 1 results obtained in our titrations of simple salt solutions are shown in Table 2 2 Our results obtained in KCl, NaCl, and NaCl/MgCb, all at 0.71 m formal ionic strength and 25.0 C are in generally good accord The range of values obtained for log is only 0.0147, and if our first titration result in NaCl is excluded, our final three experiments exhibit a range of only 0 0070 log units. The log 1 result for BCG selected for use in subsequent descriptions of S= 35 sea water was the value log 1 = 4.4166 (2 18) obtained in synthetic sea water (0.528m NaCl and 0.060m MgCb). This result compares well with the previously reported result of Byrne et al. (1988), log 1 = 4.435, and the result of King and Kester (1989), log = 4.410 + 0.007 The result of Byrne et al. (1988) was obtained in combined spectrophotometric/potentiometric titrations with a pH electrode calibrated on the free hydrogen ion concentration scale with TRIS buffer. The results of King and Kester (1989) are reported on the free hydrogen wn concentration scale and were determined through spectrophotometric measurements in artificial sea water. The results shown in Table 2.2 indicate the presence of protolytes in our synthetic solutions at concentrations on the order of 2 12 }lm The presence of such protolytes in synthetic salt solutions has been described by Ciavatta (1962), Hansson (1973)

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Figure 2.2 Residual Sum of Squares (RSS) vs. log 1 for the Mg/NaCl mixed salt data set. A value of 4.4166 is defined by the minimum residual sum of squares.

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0 0 C") 0 N 0 0 'f..; 53 c:l. .... C) 0

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Table 2.2 Best fit values from four separate salt solution experiments (25 oc). Salt type log rJ3t log oJ3t NaCl 4.4306 5.001 NaCl 4.4229 > 6.5 12.5 + 0.0 KO 4.4159 4.585 1.57 + 0.2 *NaCl/MgClz 4.4166 4.722 5.8 + 0 1 *Mole ratio of Na/Mg = 8 8 [same as sea water] Ionic strength of all the above solutions = 0.71 m. + value represents standard error at 95 % confidence level 54

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55 and Bradshaw and Brewer (1988b). The concentration of protolyte impurities found in our work are quite similar to the average impurities levels detected by Bradshaw and Brewer (1988b), DT,... 12 Jleq/L, in titrations of NaCl. The existence of protolytic impurities is readily observable when electrodes are standardized by addition of strong acid to strong electrolytes In the course of such standardizations over a period of 20 years we have noted that impurity levels up to 10-20 J.teq/kg are a common feature of synthetic sea waters and concentrated salt solutions Determinations of FP 1 Two determinations of FP 1 in natural sea water (S=35, t=25 C) yielded the results FP1 = 414.5 molal-1 and 421.7 molal-1. Our average result, FP1 = 418.1 3 6 m-1, is compared with the potentiometric results of others in Table 2 3. It should be noted that our pp 1 result is correlated with our choice of 1P 1 (log 1P 1 = 4.4166) appropriate to sea water. As an example, if our titrations in N aCl/MgCh had produced a log 1P 1 value as low as 4.410, then our calculated FP 1 result would have been reduced to 412. A FP 1 value such as 408 (Dickson and Riley, 1979) would be consistent with the result log 1P 1 = 4.4058 Sea water titration results The results obtained for s P 1 o P 1 and DT in three titrations of sea water (S=35, t=25 oc) are shown in Table 2.4. Our Table 2.4 results were obtained with log 1P 1 set equal to 4.4166 and log FP 1 = 2 6213. The average sP1 value obtained in our analyses, sP1 = 12.69,

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Table 2 3 Comparison of selected values of 1 corrected to 25 oc and S = 35 Investigation This study ......................................... ........ ..................... 418 1 Culberson (1981) ... ....... .............................. ..... ......... .404 Dickson and Riley (1979) ...... ........ .. ........................ 407 8 Bates and Culberson (1977) .............. .... .... ...... .... .. .414 Culberson et al. (1970) ........................................ .. .. .400* for S = 34. 6 56

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Table 2.4 Best fit values for S = 35 sea water at 25 oc [log IJ31 = 4.4166] Data set 1 2 3 Average 12.40 + 0 072* 12 .72 + 0.057 12 96 + 0.033 12.69 log oJ3I 4.954 + 0 06 5 152 + 0.05 5.155 + 0.02 5.10 DT /jlmolal 14.4 + 0.3 11.8 + 0.2 14.4 + 0 1 13. 6 57 + values represent asymptotic standard errors from each titration data set. Aliquots from the same sample of sea water were used in each experiment.

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58 is in reasonably good agreement with the estimates obtained for sJh in a variety of published studies summarized in Table 2.5. Our averaged s (31 estimate is in closest accord with the estimates of Bates and Culberson (1977) and Bates and Calais (1981). It should be noted that our calculated s (31 result, like Fl31, is correlated with our choice of 1(31. Whereas the result log 1(31 = 4.4166 leads to the result s(31 = 12.69, a value of log s(31 = 4.410 (King and Kester, 1989) produces the result s (31 = 11.99. The DT results obtained in our sea water titrations are in reasonable agreement with the range of protolyte concentrations (0 < DT < 21 jleq/kg(sw)) proposed by Bradshaw and Brewer (1988a) as an explanation for discrepencies between titrametric C02 determinations in sea water and C02 determinations obtained through coulometry and manometry. The o (31 results, shown in Table 2.4, are approximately an order of magnitude smaller than the protonation constants required to create the analytical anomalies described in the Bradshaw and Brewer (1988a) analysis. Although our results are not concordant with Bradshaw and Brewer (1988a) results in all respects, our work does lend some evidence to their contention that uncharacterized protolytes create problems m titrametric analysis of marine C02 systems. Since dirt acid concentrations and protonation characteristics may vary both temporally and spatially, quantitative asssessment of the contribution of dirt acid(s) to sea water alkalinity determinations is, potentially, a very challenging problem. Fortunately, both our work and the observations of Bradshaw and Brewer (1988a) suggest that for pH < 4, dirt acids in sea water should be essentially fully

PAGE 75

59 Table 2.5 Comparison of values of s p 1 at 25 oc in S = 35 sea water. This study Millero (1986) Bates and Calais (1981) Bates and Culberson (1977) Khoo et al. (1977) Culberson et al. (1970) Dyrssen and Hansson (1972 3) sP1 units are [mol/kg(water)]-1 12.69 12.3 12. 5 12.46 11.9 12. 1 11.3

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60 protonated. Consequently, the contribution of 'dirt acids' to the total alkalinity in one step alkalinity determinations (Culberson et al., 1970) can be treated in a manner analogous to the treatment of silicic acid (and other weak acids) Our averaged 1 results in Table 2.4 indicate that for one step additions of acid to sea water such that the final pH < 3 7, dirt acids will be at least 96% fully protonated. Therefore, in subsequent developments, our excess acid term (ie., (H+)T in eq. (2.1)) will include only the species H+, HS04-, HF, and HI. Calculation of excess hydrogen ion concentrations The total excess hydrogen ion concentration in this work (equation 2.1) is defined as (H+)T = [H+]T + [HI-] where, (2 19) [H+]T = [H+] + [HS04-] + [HF] = 10-PHT (2 20) pHT =log + log {(R-e1)/(e2-Re3)} -log (1 -Q) (2.22) and Q is a term which can be explicitly written as Q = { + [H+]-1)] + + [H+]1)] }/ (1+ + FT) (2.24)

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61 Although equation (2.22) appears somewhat complex, the term log (1Q) is of minor significance in normal sea water titrations. The magnitude of -log (1 Q) as a function of pHT is shown in Figure 2.3 For solutions having a pH > 3.7 (pHT > 3.56) it is readily shown using equation (2. 24) that -log (1-Q) < 0.001. Noting that [H+]T = 10 -PHT, the consequence of ignoring the term log (1 Q) at pHT = 3.56 is an error in [H+]T of 0.62 Jlmol/kg(sw) Our log 1P 1 T results obtained using equation (2.23) are shown m Table 2 6. It should be noted that although s p 1 and FP 1 results are strongly dependent on the log 1P 1 value used to relate free hydrogen ion concentration and absorbance ratios (equation 2.5), our s p 1 T results are not. Due to the strong correlation of both s P 1 and FP 1 with log 1P 1, out titrations in natural sea water produced 1P 1T values which were very weakly dependent on our choice of log 1P 1 Variations in log 1P 1 between 4.400 and 4.440 produce log 1P 1 T estimates which range between log 1P1T = 4.2696 to 4.2703 Salinity dependence of 1P 1 T In order to provide a working method for determinations of sea water alkalinity it is necessary to describe the influence of salinity on calculations of pHT. Our examinations of the influence of salinity on pHT calculations were performed within the pH range 3.4 < pH< 4 1 (pHT range 3.3 < pHT < 4.0) Under these conditions -log (1 Q) is < 0 .002 and to a very good approximation pHT can be calculated using a truncated form of equation (2 22): pHT =log 1P1T +log {(R e1)/(e2-Re3)} (2 22')

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Figure 2.3 pHT vs log (1 -Q) over the useful indicating range of bromocresol green at S = 35 and t = 25 C. At this salinity and temperature the relationship between pHT and -log(l -Q) can be described by the function log (1 Q) = 2.5705 to-(0.95967pHT)

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6 3 r--------------------------------------------------------0 It) 0 0 0 It) 0 It) 0 It) oM C") N N ,.... ,.... 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ci 0 ci ci ci ci ci (O 601-

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64 Using acidified, purged S = 35 sea water (at 3.3 < pHT < 4.0) we initially calculated pHT using equation (2.22'). We then calculated an initial [H+]T as [H+]T = 10-PHT. Upon adding deionized water to our acidified sea water sample new [H+]T values can be calculated from volumetric dilution factors Thus, through an initial measurement of pHT using equation (2.22') at 25 C and S=35, and subsequent observations of pHT and R for the diluted samples, we obtained log IJ3I T as a function of salinity (Figure 2.4 ). The best fit linear regression of our Figure 2.4 data yields log IJ3IT =log IJ3IT(S=35) + (2.578 x10-3)(35 S) (2 25) Subsequently, using equations (2.23) and (2 25) and the variation of s J3I with salinity reported by Millero (1986), we determined the salinity dependence of log IJ3t. log IJ3t =log IJ3I(S=35) + (5.380 x10-4)(35-S) (2 26) At 25C, log IJ3I T(35) = 4 2699 and log IJ3I(35) = 4.4166. It is seen that log IJ3t is very weakly influenced by salinity (within the range 20 < S < 35) compared to log IJ3I T. In the absence of data describing the salinity dependence of FJ3I, equation (2.26) was developed assuming FJ3I = 418 1 m-1. Given the small magnitude of FJ3tFT compared to s J3I ST, this should represent a satisfactory approximation

PAGE 81

Figure 2.4 log 1 T vs Salinity (at 25 C) obtained from dilutions of sea water with pure water. Linear regression of these 39 points (representing five experiments) yields log 1 T = log 1 T(35) + 0 002577(35 S); r2 = 0 967. At 25 C, log 1 T(35) = 4.2699.

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1-T""" c:l. C) 0 4.290 4.285 4.280 4.275 4.270 4 265 -'------r-----r----"""T""----y---.-----.------, 29 3 0 3 1 3 2 3 3 34 3 5 3 6 Salinity 0'1 0'1

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67 Table 2.6 Calculated log 1P 1 T values* at S = 35 and 25C determined using the s P 1 results given in Table 2.4. Data set log 1P1 sP1/ (m1 ) log 1P1 T 1 4.4166 12.40 4.27256 2 4.4166 12.72 4.26965 3 4.4166 12.96 4.26748 average 12.69 4.2699 Calculated from equation (2 23) log 1P1T = 4.4166 -log {1+ sP1ST+ FP1 FT} where ST = 0.02927 m; FT = 7.26 x 10-5m; and FPt = 418.1 m-1

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68 Temperature dependence of pHT measurements Our observations of the dependence of absorbance ratio measurements (R = 616A/ 444A) on temperature are shown in Figure 2.5. Our observations of R in acidified sea water can be summarized as ; R(25) = R(t) {1 + (0 .00907)(t250C)} (2 27) where t IS the temperature (in degrees Celcius) of the solution m which R(t) is measured Our measurements indicate that if pHT evaluations are to be precise to 0 001 pH units then temperature should be maintained at 25 0 0 2 oc or better. For any temperature excursions from 25.0 C we recommend using equation (2.27) to correct R(t) measurements to R(25) Sea Water Alkalinity Determinations A summary of the equations and calculations needed to determine pHT and total alkalinity from absorbance measurements IS shown in Appendix 2. In order to test the precision of our spectrophotometric alkalinity procedures we performed seven single-step titrations of S = 35.171 sea water at 25. 0 C. Our sea water sample was titrated to a lower pH than we generally recommend in order to test the effectiveness of our method under less than optimal conditions In order to simplify addition of the acid and BCG indicator we recommend using a combined HCl-BCG stock acid. Such a mixture can be prepared by adding a known quantity of

PAGE 85

Figure 2.5 Plot of R(25)/R(t) vs. temperature R(25) is R(t) at 25 C. R(t) = 2Af1 A [1 A = absorbance at 444nm and 2A= absorbance at 616nm] where 18 oc < t < 32 oc. R(25) can be calculated from R(t) using equation (27), [r2 = 0.989, n= 53 R(25) = R(t) { 1 + (0.00907)(t 25)}

PAGE 86

-a: --ll) (1,1 a: 1.06 1 .04 1 02 1.00 0 .98 0.96 0.94 ........ 1 8 2 0 2 2 24 2 6 2 8 3 0 32 temperature /(Celsius) -.1 0

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7 1 indicator directly to a standardized HCl solution. [Alternatively this stock HCl-BCG mixture can be standardized after indicator addition usmg Na2C03 and the BCG endpoint, Guenther (1968)]. Our mixed acid/indicator titrant was the equivalent of a solution 0 20077 molal m HCl and 1.937x10-4 molal in I-2 (BCG). Approximately 1 3 mL of our standard HCI/BCG mixture was placed in a 150 mL tared flask and the weight of added HCl was recorded. Next 100 mL of sea water was pipetted into the flask This solution was then placed in a 25.0 C water bath and purged with N2 for at least 5 minutes. Next a 100mm pathlength cylindrical spectrophotometer cell was flushed and filled with the acidified degassed sample and placed in a thermostated spectrophotometer compartment. After allowing several minutes for ree s tablishment of thermal equilibrium absorbance measurements were made at 444, 616 and 750nm. Since bromocresol green does not appreciably absorb at 750nm, absorbances at 750nm were monitored to detect any baseline shifts. Through our mea s urements of R V s. Va, plus salinity and temperature, (T A)s wa s calculated using equations (2. 1) and (2.18) through (2 27). The results of our analyses are shown in Table 2 7. Our calculated total alkalinities in the final column of Table 2. 7 have a range of 4 3 J.Leq/kg(sw) Six of the seven measurements have a range of 2.4 J.Leq/kg(sw )

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72 Table 2. 7 Replicate measurements on sea water (S = 35.171) using a one step acid addition. Total alkalinity is expressed as meq/kg(sw). Replicate Mass of HCl /(g) 1 1.3459 2 1.3633 3 1.3787 4 1.3485 5 1 .3836 6 1.4040 7 1.3382 R(25) 0.4547 0.4010 0.3668 0.4494 0.3554 0.3179 0.4813 final pHT 3 .575 3.519 3.479 3 .570 3.465 3.416 3.600 Average Std. Dev. Std. Error Total alkalinity 2 .3564 2.3543 2.3559 2.3583 2 .3549 2 .3540 2 .3562 2.3557 0.0015 0 .0006

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73 Precision and Accuracy of Total Alkalinity Measurements Questions concerning the precision and accuracy of our spectrophotometric alkalinity measurements can be resolved into a number of components. The principal components which influence the precision and accuracy of all alkalinity determinations are embodied in the terms Ma, Vs and Va in equation (2.1). Equation (2 1) can be written as (TA)s = Ma Va I Vs-(H+)T Vsa Ns (2 28) Equation (2.28) consists of two parts; an acid added term, Ma Va I V s and an excess acid term, (H+ )T V sa N s. Inspection of this equation reveals that since the excess acid term will be generally small, to a very good first approximation the precision and accuracy of the calculated sea water alkalinity, (T A)s, will be directly proportional to the precision and accuracy of each of the terms, Ma, Va, and V S If each of these terms is precise, and accurate to one part in a thousand (95% confidence), then repetitive measurements of Ma, Va, and Vs should yield the results, Ma/Ma0 = 1 + 0.001; Va/Va0 = 1 + 0.001; and V s/V so= 1 + 0.001; where Ma0 Va0 and V s0 represent true values for each parameter. It can then be seen that, Ma Va/V s = Ma0Va0/V s0 (MaoV ao/V so) { (0.001)2 +(0.001 )2 +(0.001 )2 } l/2 whereby If the true value of Ma0V a0/V s0 is on the order of 2200 Jleq/kg(sw).

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then replicate determinations of Ma V a/V s should yield the result, Ma V a/V s = 2200 3 7 J.1eq/kg(sw) 74 This analysis fundamentally indicates that great emphasis must be placed on the terms Ma, Va, and V s if (TA)s is to be precisely and accurately quantified It should be noted that an individual investigator's precision in assessing the term Ma V a/V s should be somewhat better than would be obtained for independent investigators, because, for a single investigator, errors m Ma will be correlated (using a single batch of acid). In this case, an investigator' s precision would be influenced only by uncertainties m V a and V s so that the expected precision would be given as Ma V a/V s = Ma0V a0/V s0 (1 0.0014) = 2200 3.1 Jleq/kg(sw) In our analysis of errors it is instructive to examine the excess acid term, (H+)T Vsa/V s, in terms of two components, (H+)T and V sa/V s The quotient V sa/V s can be written as V sa/V s = (V s + V a)/V s = 1 + V a/V s assummg 95% confidence limits for V a and V s on the order of one part in a thousand we can calculate V a/V s = VaofV so V ao N so { (0.001 )2 + (0 001)2} 1/2 whereby Vsa/Vs = 1 + Va0/Vs0 (1 0.0014) = (1 + Vao/Vso) 1.4 xl0-3 (VaofVso) Examination of this equation reveals that for cases such that Va0/V s0 0.1 the contribution of uncertainities in V sa/V s to uncertainties in (T A)s should be virtually negligible. On this account, the absolute uncertainty in the term (H+ )T V sa/V s should be closely linked to the

PAGE 91

75 uncertainty of (H+)T. Recent work (Byrne and Breland, 1989; Clayton and Byrne, 1992) has demonstrated that spectrophotometric measurements are capable of providing a level of precision in pH determinations which is very rarely inferior to 0.002. In general we would estimate the precision of spectrophotometric pH measurements as 0 001 units If our precision were as poor as 0.002 pH units, it follows that the absolute uncertainty in [H+]T would be approximately 0.5 jleq/kg at pHT = 4.0, and at pHT = 3.3 the absolute uncertainty in [H+]T would be roughly 2.3 Jleq/kg. For a typical level of precision in pH on the order of 0.001, the excess acid term, (H+)T V sa/V s, should be precise to approximately one jleq/kg(sw) even at pHT 3.3 In the case that alkalinities are pursued solely through gravimetric analyses, Va and V s can be made precise to approximately one part in ten thousand. Through coulometric analysis it should be possible to define Ma to a precision of approximately 2 parts in 10,000 (A. Dickson, personal communication). The overall accuracy of the added acid term would then be MaVa/Vs = Ma0Va0/Vs0 (1 .00024). If MaoV ao/V so = 2200 Jleq/kg(sw) then replicate measurements should produce the result Ma V a/V s = (2200 0.55) jleq/kg(sw). If the final pHT of the acidified degassed sea water is within the range 3.7 < pHT < 4 0 then it should be expected that the excess acid

PAGE 92

term should be precise to approximately 0.5 consequently, through laboratory-based, gravimetric analysis we expect that alkalinity determinations can be made precise to approximately one microequivalent/kg(sw) We would expect that the accuracy of careful alkametric analyses should be roughly commensurate with the precision of the analyses. Submitted to Deep-Sea Research (October, 1991) 76

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Introduction CHAPTER 3 DETERMINATION OF SEA WATER ALKALINITY BY DIRECT EQUILIBRATION WITH CARBON DIOXIDE Shipboard measurements of total alkalinity are very demanding. Currently used procedures invariably involve 77 painstaking measurements of combined titrant-acid and sea water volumes, as well as careful standardizaton and storage of acids. Most measurement procedures require frequent calibrations of pH electrodes and well behaved potentiometric systems in electrically and mechanically noisy environments We have recently observed that spectrophotometric measurements at sea (Byrne and Breland, 1989; Clayton and Byrne, 1992) using double beam spectrophotometers and multiwavelength measurements (Byrne, 1987) provide highly precise and convenient determinations of sea water pH. Spectrophotometric pH measurements involving observations of absorbance ratios are inherently calibrated, thereby obviating periodic buffer standardizations (Byrne et al., 1988). In this work we have combined spectrophotometric pH measurements with sea water pC02 equilibr a tions for the purpose of demonstrating the precision and remarkable convenience of C02 equilibration

PAGE 94

methods in determinations of sea water alkalinity. Our reported procedures increase the precision of previous C02 equilibrium alkalinity measurements (Keir et al., 1977) by a factor of ten. Theory 78 The total alkalinity of sea water (TA) can be described (Millero, 1979 Dickson, 1981 and Butler, 1982) in terms of component alkalinity contributions using the equation, where brackets, [ ] denote total concentrations of each indicated species, and L [P ] is the sum concentration of all other proton acceptors in sea water includ i ng, for example, H3Si04and HP042-. C02 gas exchange does not alter the total alkalinity of a solution (Gieskes 1974) Exchange of C02 with a sea water sample alters the distribution of species on the right side of equation (3 .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, [HC03-] becomes the dom i nant alkalinity term m equation (3 .1 ), accounting for all but approximately 0.05 % of the total alkalinity Through precise measurement of solution pH and pC02, the total alkalinity of the equilibrated sea water sample can be determined by summing the component terms in equati on (3 1) The individual terms in equation (3.1) are given as follows : (3 .2)

PAGE 95

79 (3.3) where Ko is the equilibrium constant for C02 gas exchange (Weiss, 1974 ): (3.4) and the dissociation constants K 1 and K2 (Dickson and Millero, 1987) are defined as and Borate alkalinity m equation (3.1) is calculated as [B(OH)4-] = BT KB I (KB + [H+]) where BT, the total boron concentration m sea water, is directly proportional to salinity, and KB is defined (Dickson, 1990) as KB = [B(OH)4-][H+] I [B(OH)3]. (3.5) (3.6) (3.7) (3.8) At pH less than 6 the hydroxide alkalinity, [OH-] is vanishingly small compared to the principal terms in equation (3.1). The hydrogen ion concentration term, [H+], is evaluated spectrophotometrically (Byrne, 1987; Breland and Byrne, 1992) as

PAGE 96

80 pH = -log [H+] = log 1K2 + log { (R et) I (e2 Re3)} (3.9) where 1K2 is the dissociation constant of the sulfonephthalein indicator used in this study, bromocresol purple (BCP): and the constants e1, e2, and e3 in equation (3.9) are molar absorptivity ratios (Byrne, 1987) Spectrophotometric (3.10) determinations of solution pH with BCP indicator involves absorbance measurements at 589 and 432 nm, the wavelengths of maximum absorbance of the 12-and HIforms of the indicator. The absorbance ratio, R, in equation (3.9) is then given as: R= 5s9AI432A. Measurement of absorbance characteristics of 12-at high pH and HIat low pH, provides the following absorbance ratios at 25 C : e1 = 589CHI I 432CHI = 0.00381 e2 = 589CI I 432CHI = 2.8729 e3 = 432 I 432CHI = 0.05104. Measurement of the bromocresol purple dissociation constant at 25 oc over a range of salinities (S= 29-35 2) yielded the following results (Breland, 1992) ; log 1K2 =-5.8182 + 1.292x10-3 (S-35) (3 11) where S IS salinity, and 1K2 is expressed m mol/kg(sw)

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Alkalinity contributions from phosphate and silicate can be determined from total phosphate and silicate concentrations in a manner closely analogous to calculation of [12-], the alkalinity contribution from the bromocresol purple indicator, 8 1 (3.12) Through our C02 equilibration procedures, [I2-] is included in the equation (3.1) summation term, 1: [P-], and equation (3 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. The relationship between the sea water's initial alkalinity (TA)i and the sample's final measured alkalinity (TA)r is (3.13) where Vi and Vr are initial and final masses (or volumes), and the term IT V f follows from the addition of indicator (alkalinity) as dissolved Na2I 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 located at 489.5nm it follows that IT = 489.sA I (D 489.sE) (3.14)

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82 where 489.sA is absorbance at 489.5nm, D is pathlength (in em) and 489.sE is the indicator's molar absorptivity at the isobestic point: 489.st = 7350 cmlM-1. Measurement of total alkalinity through C02 equilibration procedures requires precise knowledge of the C02 partial pressure The partial pressure of C02 at equilibrium is calculated from the relationship pC02 = (AP VP(sw)) Xco2 (3.15) where AP is atmospheric pressure at the time of equilibration, and Xco2 is the C02 mole fraction in the equilibration gas Sea water vapor pressure VP(sw). is calculated from the equation (Riley and Chester, 1971 ) VP(sw) = VP(w) [1 (0.0005364 )(S)] (3.16) where VP(w) is the vapor pressure of pure water at the equilibration temperature, and S is salinity VP(w) at 25 C is 23.756 Torr (760 Torr = one atmosphere = 101,325 Pa). Atmospheric pressure (AP) can be determined with a mercury barometer, using the following equation, AP = Ho g(S) PHg0 (3.17) where Ho is the height of the mercury column (in em) corrected to

PAGE 99

83 0 C, g(S) is the gravitational acceleration at latitude (9), and P Hg0 is the density of mercury at 0 C. P Hg0 equals 13.5951 g/cm3 Calculation of g(e) is made utilizing the relationship, [Press and Siever (1986), p 493]. g(S) (in cm/sec2) = 978.049 [1 + 0.0052884 sin2 (9) 5.9 x10-6 sin2(29)]. Methods (3.18) Sea water samples (8=35 217) were equilibrated in a round bottom flask attached to a rotary evaporator. The flask, containing 100mL of sea water 20 J..Lmolar in BCP) was partially submerged m a water bath and rotated at 2 4 revolutions per second. A refrigerated thermocooler (Lauda model #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 C02 gas into the head space of the reaction flask, just above the gas liquid interface. The flow of thermally equilibrated C02 was regulated at 50 cm3 /min with a Manostat precision flowmeter (model #36 541 035). The flask head-space was open to the atmosphere at a point 30cm above the sample. A peristaltic pump (Cole-Palmer model #7520 25) continuously circulated equilibrated sea water between the rotary evaporator and a 10mm in line spectrophotometer flow cell. The

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84 flow-rate of circulating sea water was approximately 0 6 mL per second. The transfer tubing (1/8 I.D. PEP Teflon) plus flow cell volume was approximately 20mL. Absorbance measurements were made with a Cary 170 spectrophotometer. Temperature was monitored throughout the equilibrations using a calibrated precision thermometer. The basic form of bromocresol purple (12-) has an absorption maximum at 589nm and the acidic form (HI-) has a maximum at 432nm. An additional absorbance reading at 750nm, where BCP is non-absorbing, 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 (489.5nm) is used to calculate IT. Atmospheric pressure determinations were made using a standard mercury barometer (Welch Scientific #1215). At the latitude of our USF laboratory (9 = 27 46'), g(e) in equation (3 .17) was equal to 979.1676 cm/sec2. Corrected atmospheric pressure values were periodically compared with those of a local airport (Albert Whitted FAA tower) located less than one kilometer from our laboratory. Pressure differences (airport vs laboratory) were never greater than 67 Pa and averaged 19 Pa. Humidification of the equilibration gas was achieved by passing the C02 gas mixture through a bubbling frit (pore size C) submerged in several centimeters of deionized water. The gravimetrically determined C02 mole fraction of the primary standard C02/N 2 gas mixture employed in our equilibration experiments (Air Products and Chemicals, Inc.) was 0.29996s
PAGE 101

Results and Discussion The procedure used to calculate (T A) through C02 equilibrations is outlined in Table 3.1. The directly measured parameters in our sample calculations are: Xco2 = 0 29996s 85 0.00001; H (24.0 C) = 765.0mm; R (25 oc) = 0.8500; S = 34. 5; 489.sA(25 C) = 0.1600. Equilibrium data were obtained as follows: salinity dependence of Ko (Weiss, 1974); salinity dependence of K1 and K2 (Dickson and Millero, 1987); salinity dependence of 1K2 (equation 3.11); salinity dependence of Ks (Dickson, 1990). The H/H0 temperature dependence is usually given by the barometric instrument manufacturer. Standard barometer-temperature correction tables are given in Dean (1973). The results of 8 replicate alkalinity measurements on Gulf of Mexico surface water are shown in Table 3.2. Our measurements, made over a ten day period, had a standard deviation equal to 0 .89 J.Leq/kg(sw) 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 al. (1977). The coefficient of variation given by Keir et al. (1977) on 10 replicate samples was 0.36 % which, assuming a (T A) of 2.3 meq/kg, yields a s tandard deviation of 8.3 J.Leq/kg. The substantially improved precision obtained in the present work is attributed to two factors: (a) improved reproducibility in measur e ments of pH and (b) improvements m the reproducibility of COz sea water equilibrations. Our previous work has demons trated that spectrophotometric pH replicates at sea

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86 Table 3.1 Calculation scheme and values calculated from primary data. Primary Data VPw = 23 756 Torr (25 oc, S=34 5) H (24 oq = 765.0mm Xcoz, VP(sw) AP s 489 .sA R S pC02 pH, Ko. K1 pC02, pH, Ko K1. K2 S pH S, pH 489 5A [HC03-J, [C032-J, [B(OH)4-J, [12-], [H+] Calculation Procedure eq. 3.16 correction tables eq 3.17 eq 3 .15 eq. 3 .11 eq. 3.14 cq 3.9 eq 3 2 eq. 3.3 eq. 3 7 eq 3 12 & 3 14 eq. 3 1 Vi= lOOmL, Vf = 100 1mL, IT eq 3 .13 Derived Data VPsw = 23 32 Torr H0 = 761.88 mm AP = 760 .71 Torr = 1.00094 atm pC02 = 0 29104 atm log 1K2 = -5.8189 IT = 2.18 x1o-5 Molar = 2 .13 x 1o-5 pH= 5.2946 [HC03-] = 2 3189 x10-3 [B(OH)4-] = 2.17 x10 7 (TA)f= 2.3199 xtQ-3 (TA)i = 2 3009 x10-3 All concentration units in mol/kg(sw) unless otherwi s e noted

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Tab l e 3.2 Replicate Day 1 Day 1 Day 1 Day 3 Day 8 Day 8 Day 10 Day 10 Average St. Dev. Std. Error c.v. 87 Measurements of sea water alkalinity (S = 35.217, 25 C) made ove r a period of 10 days. pC02 *pH [HC03 ] (TA)f (TA)i /atm /mol/kg( s w) /meq/kg(sw) /meq/kg( s w) /meq/kg(sw) 0.29098 5.302 5 2 3663 2 .3 677 2 .34825 0 29082 5 302g 2.3668 2.3682 2.3487 0.29074 5.303o 2 .3674 2 .3689 2.3494 0.29095 5.302 7 2.3672 2.3686 2.3491 0.29188 5 .3 00g 2.3648 2.3662 2.3467 0.29110 5.3024 2 .3 667 2.3680s 2.3486 0.29127 5.302} 2 3668 2.3682 2 3487 0.29114 5.302 5 2.3676 2.3690 2.3495 2.36670 2.3681} 2.34861 0 00087 0 .00089 0.00089 0 0003 1 0 00029 0.0003} 0.037 % 0.037 % 0.038 % [H+] = [H+]f + [HS04-] + [HF] where [H+]f = 'free hydrog e n ion concentration (Dickson and Millero, 1987)

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88 typically agree to within 0.0005 pH units. Spectrophotometric pH measurements are quite rapid compared to potentiometric measurements and do not require the use of buffer standardizations (Robert-Baldo et al., 1985; Byrne and Breland, 1989). The improved reproducibility of C02sea water equilibrations in our work is principally attributed to elimination of bubbles in our equilibration procedure. Bubble stze spectrum and bubble depth can exert a strong influence on effective gas partial pressure. Keir et al., (1977) acknowledged that determination of the equilibrium pC02 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, u sing titrametric procedures i s a subj ect of current conc e rn and controversy. Laboratory intercalibrations (UNESCO, 1990, 1991, Poisson et al., 1990) have shown that the reproducibility of measurements made by individual laboratories is considerable better than the agreement among laboratories. As a consequence of such studies it has been recommended that standard reference materials including alkalinity stand a rds, be prepared and distributed to participants of the global oc e anic carbon program. The procedures we recommend for assuring the accuracy of alkalinity measurements at sea are closely tied to the use of standard reference materials. Since [HC03-] constitutes approximately 99.95 % of the total alkalinity, (TA)r, in our equilibrium procedures (Table 3.1 ), the accuracy of our alk a linity measurements will be very closely related

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89 to measurement of this dominant term. Inspection of equations (3.2) and (3.9) shows that bicarbonate alkalinity can be expressed in logarithmic form as follows: log [HC03-] =log (KoKthK2) +log pC02 +log {(R-el)/(e2-Re3)} (3.19) the term log (Ko K 1hK2) 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 [HC03-], we recommend that assessments of log (Ko K tf1K2) be obtained by each investigator in a manner which correlates log pC02 measurements with log (Ko K tf1K2) It follows from our previous discussion that, usmg a standard solution having alkalinity (TA)s, we can write (3. 20) where [HC03-] s denotes bicarbonate alkalinity of the standard solution at equilibrium. Subsequent to calculation of [HC03] s using equations 3.20 and 3.1 3.12, the bicarbonate alkalinity can be described using equation 3.19, wherein log (KoKtf1K2) is treated as the only unknown In this manner the critically important calibration term log (KoK tf1K2) becomes correlated with each investigators procedures for determining pC02. According to this procedure, the term KoK 1hK2 is determ i ned as a single entity whereupon any uncertainties in the individual terms Ko, K1, and 1K2 are not cumulative.

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90 The method which we used to determine 1K 2 was very similar to the procedure we have outlined above. The term (T A)s was carefully determined on a sea water sample through acid titrations. Subsequently, through iterative calculations we determined the value of 1K2 which satisfied equations 3 2, 3.3, 3.8-3.12, 3 19 and 3 .2 0 Following this procedure the 1K2 results given in equation (3.11) are consistent (correlated) with the product KoK 1 calculated using the Ko results of Weiss, (1974) and the K1 results of Dickson and Millero, (1987) Combining our 1K2 results (equation 3.11) with salinity corrected values for Ko (Weiss, 1974) and K1 (Dickson and Millero, 1987) we obtain the following estimate (25 C) for the salinity dependence of the term (KoK1hK2) : log (Ko K 1hK2) = -1.574 + 6.06 x10-4 (S-35) (3.21) Total alkalinity standards for measurements of sea water alkalinity are expected to become routinely available from Scripps Institution of Oceanography (UNESCO, 1991) Although future work may demonstrate that measurements of the term KoK1hK2 are sufficiently consistent among various investigators that standard values for this calibration term might be adopted, at the present time w e consider the use of alkalinity standards to me as ure this term at sea a critically important aspect of equilibrium alkalinity determinations. The methods which we have outlined are extremely simple m a n operational sense. It is our expectation that the fundamental simplicity of these equilibration procedures may provide an

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91 improved coherence m 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 Submitted to Analytical Chemistry (January, 1992)

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92 SUMMARY Spectrophotometric methods are rapid and easy to use and, as demonstrated in Chapter One, are capable of providing high prec1s10n pH determinations at sea. The methods used to determine pH in my dissertation are quite similar for all indicators in the su lfonephthalein group. Sulfonephthalein indicators are applicable to pH measurements within the range 1.5 < pH < 9.5. Sulfonephthalein indicators are inherently calibrated. The absorbance properties and equilibrium characteristics of these indicators are molecular properties, and need not be referenced to the molecular properties of pH buffers. Refinements in indicator formation constants and molar absorptivity coefficients, will not lessen the quality of archived spectrophotometric pH data. In fact, pH data preserved in the form (R, S, T, indicator identity and concentration) will improve in accuracy (with undiminished precision) if changes to pK2's, (dissociation constants) or molar absorptivity coefficients are ever required. This is a major advantage of spectrophotometric pH determinations for long term studies of ocean pH and alkalinity There are several advantages to using C02 gas mixtures m sea water titrations. The use of C02 gas equilibration techniques provides a means of correlating indicator pK with the dissociation constant behavior of carbonic acid. My Chapter Three equilibration

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93 procedures can be used to provide indicator pK's which directly, precisely and accurately relate total C02, total alkalinity and the pC02 of sea water. My C02 titration methods are readily amenable to processing many samples simultaneously in alkalinity determinations at sea. Carbon dioxide gas standards can be prepared and certified by a central facility and used worldwide. The stability of such standards should be superior to the stability of solution buffers and standard acids. [The composition of a compressed gas does not change appreciably over time.] Four parameters are commonly used to determine the state of the carbon dioxide system of sea water: pH, alkalinity, pC02 and TC02. Determining any two of these parameters allows calculation of the remaining two and provides a complete description of a sample's dissolved C02 system. Thus, the pC02 of a sea water sample can be obtained from measurements of pH and alkalinity. If pH is precise to 0.01 pH unit and TA is known perfectly, the propagated error in a sample's calculated pC02 would be on the order of 2.3% It is then clear that spectrophotometric pH measurements (which are precise to approximately 0.001 at sea) offer significant advantages over less reproducible potentiometric measurements. The techniques for measurement of pH detailed in this dissertation should permit calculations of pC02 from TA and pH which are precise to approximately 0.15 %. [For the purposes of this calculation I assumed pH precision equal to 0.0005 pH unit (Chapter 1) and TA precision equal to 0.04% (Chapter 3) ] This level of precision in pC02 is identical to the desired accuracy in pC02 proposed by the JPOTS panel on oceanic C02 measurements (UNESCO, 1991 ).

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94 The flexibility of pH and alkalinity measurement techniques should allow oceanographers to monitor oceanic C02 invasion in much more detail than previously possible. The simple, rapid and precise alkalinity methods examined in this dissertation are readily applicable to remote measurements. Spectrophotometric pH procedures offer great potential for in-situ measurements at great oceanic depths and, as well, autonomous measurements on free drifting or moored buoys.

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95 LIST OF REFERENCES Anderson D. H. and R J. Robinson (1946) Rapid electrometric determination of the alkalinity of sea water using a glass electrode Industrial and Engineering Chemistry, Analytical edition, 18:767-769. Anderson, L. and M. Wed borg (1983) Determination of alkalinity and total carbonate in sea water by photometric titration Oceanologica Acta, 6: 357-364. Anderson, L. and M. Wedborg (1985) Comparison of potentiometric and photometric titration methods for determination of alkalinity and total carbonate in sea water. Oceanologica Acta, 8: 479-483 Anfalt, T., A. Grnaeli and M. Strandberg (1976) Probe photometer based on optoelectronic components for the determination of total alkalinity of sea water Analytical Chemistry, 48: 357-360. Banyai, Eva (1972) Chapter 3, Acid-base indicators; in Indicators. E. Bishop, ed., Pergammon Press, Braunschweig, Germany : International Series of monographs in Analytical Chemistry, 51Indicators ; R Belcher and H Frieser, general editors. Bates R.G and J .G. Calais (1981) Thermodynamics of the dissociation of Bis-H+ in sea water from 5 to 40 C. Journal of Solution Chemistry .l.Q.: 269-279

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Bates R.G. and C H. Culberson (1977) Hydrogen ions and the thermodynamic state of marine systems. In ; The Fate of Fossil Fuel C02 in the Oceans, N.R. Anderson and A. Malahoff, editors, Plenum Press, New York. 96 Boyle, Robert (1664) Experimental History of Colours, London; quoted in The Words of the Honourable Robert Boyle, Vol., II, London 1744. As cited by Rancke Madsen (1972). Bradshaw A.L., P G Brewer, D. Shafer and R T Williams (1981) Measurements of total carbon dioxide and alkalinity by potentiometric titration in the GEOSECS program. Earth and Planetary Science Letters, 55: 99-115. Bradshaw A L. and P.G. Brewer (1988a) High precision measurements of alkalinity and total carbon dioxide m sea water by potentiometric titration --1. Presence of unknown protolyte(s)? Marine Chemistry, 23: 69-86 Bradshaw A L and P.G. Brewer (1988b) High prec i sion measurements of alkalinity and total carbon dioxide m sea water by potentiometric titration -2. Measurements on standard solutions Marine Chemistry, 24: 155-162. Breland J.A. and R.H. Byrne (1992) Spectrophotometric determination of the total alkalinity of sea water using bromocresol green. (Submitted to Deep Sea Research) Breland J.A. and R.H. Byrne (1992) Determination of sea water alkalinity by direct equilibration with carbon dioxide (Submitted to Analytical Chemistry) Butler J. N. Carbon Dioxide Equilibria and Their Applications, Addison-Wesley Publishing Company, Reading, Massachusetts 1982, p 159

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Byrne R.H. (1987) Standardization of standard buffers by visible spectrometry. Analytical Chemistry, 5..2.:1479-1481. Byrne R.H. and D.R. Kester (1974) Inorganic speciation of boron in sea water. Journal of Marine Research, .3..2.: 119-127. 97 Byrne R.H., G. Robert-Baldo, S.W. Thompson and C.T.A. Chen (1988) Sea water pH measurements: an at-sea comparison of spectrophotometric and potentiometric methods. Deep-Sea Research, 35: 1405-1410. Byrne R.H and J. A. Breland (1989) High precision multiwavelength pH determinations in sea water using cresol red. Deep-Sea Research, 36: 803-810. Ciavatta L. (1962) Potentiometric purity control of salt media for equilibrium studies. Arkiv fur Kemi 20: 417-435 Clark, W. M. (1928) The Determination of Hydrogen Ions 3rd ed., Williams & Wilkins Co., Baltimore, MD Clark, W. M. and H. A. Lubs (1916) J. Biol. Chern. 25:479-509. Clark, W. M. and H. A. Lubs (1917) J. Bacteriology 2:1-34, 109-136, and 191-236. Clayton T. and R. H. Byrne (1992) Calibration of m-cresol purple on the total hydrogen ion concentration scale and its application to C02 -system characteristics in sea water. in preparation. Culberson C.H (1981) Direct Potentiometry, Chapter 6, In; Marine Electrochemistry. M. Whitfield and D. Jagner, editors, Wiley, Chichester.

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Culberson C.H., R.M. Pytkowicz and J.E. Hawley (1970) alkalinity determination by the pH method. Marine Research, 28: 15-21. Sea water Journal of Dean J. (1973) Lange's Handbook of Chemistry, 11th Edition, McGraw-Hill Book Company, New York, NY Dickson A.G (1981) An exact definition of total alkalinity and a procedure for the estimation of alkalinity and total inorganic carbon from titration data. Deep-Sea Research, 28A:609-623. 98 Dickson A.G ( 1990) Thermodynamics of the dissociation of boric acid in synthetic sea water from 273.15 to 318.15 K. Deep-Sea Research, 37 : 755-766 Dickson A.G. and J P. Riley (1979) The estimation of acid dissociation constants in sea water media from potentiometric titrations with strong base I. The ionic product of waterKw. Marine Chemistry, 78: 89-99. Dickson A. G. and F .J. Millero (1987) A comparison of the equilibrium constants for the dissociation of carbonic acid in sea water media. Deep-Sea Research 34: 173 3-17 43. Dyrssen, D. (1965) A Gran titration of sea water on board SAGITTA. Acta Chern. Scand. 19: 1265 Dyrssen D. and L.G. Sillen (1967) Alkalinity and total carbonate m sea water. A plea for p-T -independent data. Tell us 19:113-120 Dyrssen D. and I. Hansson (1972-3) Ionic medium effects in sea water A comparison of acidity constants of carbonic acid and boric acid in sodium chloride and synthetic sea water.

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99 Marine Chemistry, 1: 137-149. Edmond J M. (1970) High precision determination of titration alkalinity and total carbon dioxide content of sea water by potentiometric titration. Deep-Sea Research, 17: 737-750. Feely R.A., M Lewison, G J. Massoth, G. Robert-Baldo, J.W Lavelle, R.H. Byrne, K L. VonDamm and H.C. Curl (1987) Composition and dissolution of black smoker particulates from active vents on the Juan de Fuca Ridge, Journal of Geophysical Research, 92; 11,347-11,363. Friedenthal, H ( 1904) Z Elektrochem., 10: 113Gieskes, J.M. (1974) The alkalinity-total carbon dioxide system m sea water, in The Sea, Vol 5, Wiley-Interscience, New York, NY. Gran, G. (1952) Determination of the equivalence point m potentiometric titrations. Part II Anal ys t, 77: 661 671. Graneli, A. and T. Anfalt (1977) A simple automatic phototitrator for the determination of total carbonate and total alkalinity of se a water. Analytica Chimica Acta, 91: 175-180 Greenberg D.M., E G Moberg and E.C. Allen (1932) Determination of carbon dioxide and titratable base in sea water. Industrial and Engineering Chemistry, Analytical Edition, 4 : 309-313. Gripenberg S. (1937) The determination of excess base in sea water. InternaL Assn. Phys Oceanogr. (Assn. d'Oceanogr. Phys.) Union Geod et Geophys. InternaL, Proc .Verb. no. 2, p 150-152. Liverpool.

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100 Guenther W. B. (1968) Quantitative Chemistry: Measurements and Equilibria, Addison-Wesley Publishing Co., Reading, Mass. Hansson I. (1973) A new set of acidity constants for carbonic acid and boric acid in sea water. Deep-Sea Research, 20: 461-478. Hansson I and D. Jagner (1973) Evaluation of the accuracy of Gran plots by means of computer calculations: application to the potentiometric titration of the total alkalinity and carbonate content of sea water. Analytical Chimica Acta, 75: 363-373. Iorden E., (1632) A Discourse of Naturall Bathes. and Mjnerall Waters, 2nd Ed., London Johnson K.M., A.B. King and J.McN. Sieburth (1985) Coulometric TC02 analyses for marine studies: An introduction. Marine Chemistry, 16: 61-82. Keir R.S., S.P. Kounaves and A. Zirino (1977) Rapid determination of the "titration alkalinity" of sea water by equilibration with C02. Analytica Chimica Acta, 91: 181-187 Khoo K.H., R.W. Ramette, C.H. Culberson and R.G. Bates (1977) Determination of hydrogen ion concentration in sea water from 5 to 400C: Standard potentials at salinities from 20 to 45 Ofoo, Analytical Chemistry, 49: 29-34. King D.W. and D.R. Kester (1989) Determination of sea water pH from 1.5 to 8.5 using colorimetric indicators. Marine Chemisrty, 26: 5-20 Lewis, W., (1767) Experiments and observations on American potashes -with an easy method of determining their

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respective qualities. London. Macintyre F. (1976) Concentration scales: a plea for physico chemical data. Marine Chemistry, 4: 205-224. 101 Millero F.J. (1974) Sea water as a multicomponent electrolyte solution, In, The Sea, Volume 5; Marine Chemistry, edited by E D. Goldberg, Wiley-Interscience, New York. Millero F J. (1979) The thermodynamics of the carbonate system in sea water. Geochimica et Cosmochimica Acta, 43: 1651-1661. Millero F. J. (1986) The pH of estuarine waters. Limnology and Oceanography, 31: 839-847. Millero F J and A. Poisson (1981) International one-atmosphere equation of state of sea water. Deep-Sea Reasearch, 28A: 625-629. Mitchell, P H. and N.W. Rakestraw (1933) The buffer capacity of sea water. Biological Bulletin, 65: 437-451. Mitchell, P .H. and I.R. Taylor (1935) The dissociation constant of cresol red in sea water. Journal du Conseil (perm. intre p. l'explor. de le mer) Vol X: 169-172. Mitchell, P.H., K. Buch and N.W. Rakestraw (1936) The effect of salinity and temperature upon the dissociation of cresol red and phenol red in sea water. Journal du Conseil (perm. intre p. l'explor. de le mer) Vol XI: 183-189. Park, P. K. (1968a) Alkalinity and pH off the coast of Oregon. Deep Sea Research, 15:171-183.

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Park, P. K. (1968b) Alteration of alkalinity, pH and salinity of sea water by metallic water samplers Deep-Sea Research, 15:721-722. 102 Press F. and R. Siever (1986) Earth, 4th Edition, W.H. Freeman and Company New York NY Ramage, W. D and R. C Miller (1925) The salt error of cresol red J. Amer. Chern Soc. 47: 1230 1235. Rancke Madsen, E (1958) The Development of Titrimetric Analyses till 1806, Copenhagen Rancke-Madsen, E (1972) The History of Indicator s in Indicators, edited by Edmond Bishop, part of the International Series of Monographs in Analytical Chemistry; 51-Indicators General ed.; R Belcher and H Frieser, Pergamon Press, Braunschweig, Germany Riley J P and R. Chester (1971) Marine Chemistry, Academic Press, New York, NY Robert Baldo G., M.J. Morris and R H Byrne (1985) Spectrophotometric determinations of seawater pH using phenol red. Analytical Chemistry, 57; 2564-2567 SAS (1984) SAS OS Release 5.16, SAS Users Guide version 5 edition SAS Institute, Inc. P O. Box 8000, Cary, NC, 27511-8000. Sillen L.G (1971) Polynuclear Complexes in Solution, Chapter 9 of Coordination Chemistry Vol. 1, edited by A. E. Martell, ACS Monograph 168, Van Nostrand Reinhold Co., New York Snell, F D. and C. T Snell Colorimetric Methods of Analysis 3rd ed Vol. 1, (1948) VanNostrand and Co., Princeton, NJ

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103 Sverdrup, H. V., M. W. Johnson and R. H. Fleming, The Oceans. Chapter V ., (1942) PrenticeHall, Inc., Englewood Cliffs, NJ Szabadvary, F., (1964a) Development of the pH conceptA historical survey Journal of Chemical Education, 41; 105-107. Szabadvary, F., (1964b) Indicators--A historical perspective. Journal of Chemical Education, 41; 285-287 Thompson, T.G. and Robert V. Bonnar (1931) The buffer capacity of sea water. Industrial and Engineering Chemistry, Analytical Edition, 3: 393-395 Thompson, T.G. and D.H Anderson (1940) The determination of the alkalinity of sea water. Journal of Marine Research 3: 224 -229. Tomicek, 0. (1951) Chemical Indicators, Buttersworth Scientific Publication, London. UNESCO (1981a) Background papers and s upporting data on the Practical Salinity Scale 1978, Technical Papers in Marine Science number 37. UNESCO ( 1981 b) Background papers and supporting data on the International Equation of State of Seawater 1980, Technical Papers in Marine Science number 38. UNESCO (1990) Intercomparison of total alkalinity and total inorganic carbon determinations in sea water by A Poisson, F. Culkin and P Ridout. UNESCO technical papers in marine science; 59. UNESCO ( 1991) Reference materials for oceanic carbon dioxide measurem e nts, A Report of the subpanel on standards for

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104 C02 measurements of the Joint Panel on Oceanographic Tables and Standards UNESCO technical paper s in marine science; 60 Wallace, W .J ( 1980) The development of marine chemistry until 1900. In; Oceanography -The Past., Editors, M.Sears and D. Merriman, SpringerVerlag, Berlin. Weiss, R.F (1974) Carbon dioxide in water and sea water: The solubility of a non-ideal gas. Marine Chemistry 2 : 203215. Wells, R. C. (1920) The salt error of cresol red. J Amer. Chern Soc., 42: 21602167. West, L. E and R. J. Robinson (1941) Potentiometric analysis of sea water II. Determination of titration alkalinity. Journal of Marine Research, 4: 38 41.

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105 APPENDICES

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APPENDIX 1 Techniques for measuring the absorptivity ratios for the sulfonephthelein indicators. 106 Initial scans of the indicator (at 2-3 micromolar concentration) dissolved in 0.71m NaCl were made at several widely separated pH's in order to determine the wavelength of maximum absorption of each of the indicator forms; H2L, HL-, and L2-. Additionally titrations of the indicator with HCl were performed to determine the mv reading where the response of the HLform of the indicator was at a maximum. A Ross electrode (Orion model #810200) was calibrated on the pHT scale by titrations with HCl in the 0.71m NaCl media Nerstian behavior was confirmed. Determination of the particular components of the molar absorptivity ratios et, e2, e3 were performed in several stages. An open top 100mm quartz cell was used to allow stirring, N2 bubbling and to allow absorbance measurements to be made concurrently with mv measurements All absorbance measurements were made in the thermostated (25.0 C) cell chamber of a Cary 17D spectrophotometer. Absorbance reading were made at wavelength (1), wavelength (2) and 750nm in every case. Molar absorbances, A.tx, are calculated from the relationship A.tx = abc where a is the absorbance of the particular form, x, at the specified wavelength, A, b is the pathlength (in centimetres) and c is the concentration (molar) of the indicator.

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Appendix 1 (Continued) 107 In order to determine e2 (e2 equals 2tL I ttHL), 100mL of 0 .71m NaCl is taken to a high pH (-11.5) with NaOH and the baseline absorbance determined. Enough indicator is then added (indicator stock solution concentrations were in the range 1-5 millimolar) to make the basic NaCl solutions -2 x10-6 molar Absorbance readings were repeated at the three wavelengths Next HCl was added to obtain the optimal pH for measurement of the HLform of the indicator. Absorbance readings were then repeated at each wavelength. In order to determine et and e3, a indicator solution -20-50 micromolal was prepared in basic N aCl. The absorbance was determined at wavelength (1). Subsequently this solution was taken to the pH of maximum absorption of the HLindicator form with HCl. The absorbance at wavelength (2) was determined in the lOOmm cell. Part of this acidic solution was subsequently transfered to a 1 Omm cell. The absorbance of the concentrated acidic indicator solution at wavelength(!) was made i n the shorter pathlength cell. The ratio e3 is calculated as ItL I 1 tHL and et is calculated as 2CHL I lCHL

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Appendix 1 (Continued) 108 Table A.l. Wavelengths of max1mum absorption and extinction coefficients for various indicators indicator A.1 A.2 e1 e2 e3 444 616 0 .0054 2 .324 0 .1302 BCP 432 589 0.00381 2.8729 0 .05104 BTB 434 616 0.00371 2.2501 0.1752 PR 433 558 0.00796 2. 7 457 0.11401 CR 434 573 0 .00286 2. 7985 0.09025 mCP 434 578 0 .00668 2.2121 0.1340 BCG = bromocresol green; BCP = bromocresol purple; BTB = bromothymol blue; PR = phenol red; CR = cresol red; mCP = meta cresol purple All values are for S=35 sea water and a temperature of 250C.

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109 APPENDIX 2 This appendix outlines the information and computations required to calculate (TA)s using the spectrophotometric techniques presented in Chapter 2. Use of a computer for data processing is highly recommended A numerical example is presented below to allow the user to confirm encoding of equations The analytical procedure consists of three basic steps: 1) A known amount of standardized acid is added to a known amount of sea water sample; 2) The acidified sample is degassed with a stream of Nz gas and 3) The degassed solution is transfered to a spectrophotometer for absorbance measurements at several wavelengths. Based on our experience we comment here on a few critical elements of the methodology Sea water blank absorbance values (obtained at the wavelengths 444, 616 and 7 50) also serve as a preliminary rinse of the spectrophotometer cell prior to the introduction of acidified degassed, sample. Temperature should be controlled to 25.0 + 0 1 C, and recorded directly with each suite of absorbance measurements. Careful attention must be paid to the standardization of the acid/BCG mixture, its storage, and subsequent delivery to the sample At sea, where gravimetric methods are problematic, volumetric delivery of the acid/BCG mixture must be carefully implemented, using appropriate pipet calibrations and temperature corrections Volumetric determinations are best conducted in thermostated, calibrated glassware. Scanning spectrophotometers capable of at least + 0.001 absorbance unit

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Appendix 2 (Continued) 11 0 resolution are required (+ 0 0001 prefered). Prompt transfer of degassed sample to the spectrophotometer cell is recommended to mm1m1ze reinvasion of the sample by C02. The following information is required for (T A)s determinations. 1) Absorbances at 444, 616, and 750 nm for both the sea water (blank) and the acidified sample (containing the indicator) 2) Temperature of sample/acid mixture at the time absorbance is measured 3) Salinity of the initial sea water sample (Practical Salinity Scale; UNESCO 1981a b) 4) Volume (or mass) of the sea water sample (and transfer temperature, if pipetted) 5) Volume (or mass) of the acid/indicator mixture added to sample 6) Acid concentration 7) Indicator concentration m the HCl!BCG acid titrant (+ 10 %) 8) Variation of ST and FT as a function of salinity. STIS = 8 0686 x10-4 mol sulfate/kg(sw) and FTIS = 2 0 x 10-6 mol fluoride/kg(sw) [also see Millero (1974) or Macintyre (1976)]. Steps to be followed in these determinations are given below ; L Absorbance readings are taken (at 444, 616, and 750 nm) on a portion of the unacidified sea water sample ( A. A (blank) = absorbance blank values). II. Next, at these same wavelengths, obt a in absorbance readings for the acidified, degassed sea water sample containing the indicator A. A (sample) = J...A (indicator) + A. A (blank)

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Appendix 2 (Continued) 111 III. Record the temperature (25 + 0.1 oc is optimal). IV. A, A (indicator) is calculated and the absorbance ratio, R(t), is computed as 616A (indicator)/ 444A (indicator). Y... If the temperature of the absorbance readings is other than 25.0 C, equation (2.27) should be used to correct R(t) to R(25) VI. The salinity of the acidified sample, S(a), is calculated as S(a) = S i M i/(Mi + Ma) where Mi is the mass of the initial sea water sample having salinity Si, and Ma is the mass of the added HCl/BCG titrant. [Note: Although the concept of salinity cannot be rigorously extended to these acidified samples, the above approximation is reasonable for the degassed sample since, in essence, one bicarbonate ion has been replaced by one chloride ion during the sample acidification Thus to a first approximation the diluent can be considered to be pure water.] VII. log 1 T(s) is determined usmg equation (2.25); log = 4 2699 + 2.578 x10-3 (35 S(a)) [Note that S(a) is the salinity of the acidified sample.] VIII. log 1 (s) is calculated from equation (2.26); log = 4.4166 + 5.946 x10-4 (35 S(a)) IX. pH is then calculated using equation (2.5). X S(a) is used to calculate ST and FT (from salinity ratios) XI. s 1 for use in equation (2.24) is estimated from the salinity of the sample using the equation 1 = 24.899 0 54247(S(a)) + 5.3276 x10-3 (S ( a))2 ; [Derived from Millero (1986) and our result at S=35] Information is not available on the variation of 1 with

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Appendix 2 (Continued) 112 salinity therefore 418 1 m-1 is used for salinities such that S > 29. XII. Q is determined usmg equation (2.24 ). XIII. pHT is determined from equation (2.22) XIV. A value for [HI-] is determined from equation (2.4) and IT in the acidified sample. XV. (T A)s is now computed from equation (2. 1) m the form; (TA)s =(rna Va)/Vs((10-PHT + [HI-])Vsa)/Vs Note that the units of pHT and [HI ] are molal. Typically V s will be in units of kg(sea water) to conform to standard oceanographic practice. For purposes of permitting the user to confirm encoding equations, the following set of experimental parameters is solved for (TA)s. 1) Uncorrected absorbances at 444 616 Unaltered sea water sample 0 .0000 0.0090 Acidified degassed sea water plus indicator 0.8344 0.5000 2) Absorbances measured at temperature 24.6 C. 3) Initial salinity, S(i) of sea water is 34.948; 750 0 .0700 0.0704 [density = 1.023304 g/mL at 25 C; Millero and Poisson(1981)] 4) Vs = 100.00 mL at 25 C 5) Va = 1.345 mL at 25 C [density = 1.0018 g/mL]

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Appendix 2 (Continued) 113 6) rna = 0.20000m [equivalent to 0.19862 mol/kg(soln)1 7) IT = 2.6208 x10-6 m [addition of 1.345 mL of HCl/BCG mixture to 100mL of sea water at 25 C .]. The HCI/BCG titrant concentrations are ffiHCl = 0.20000m and IDBCG = 1.95 x10-4 m 8) From Table 2 1, e1 = 0.00131; e2 = 2.3148; and e3 = 0.1299 9) Salinity ratios for sulfate = 8.0686 x 1 o-4 mol/kg(sw)/Salinity and for fluoride = 2.0 X 1 o-6 mol/kg(sw)/Salinity [Dickson and Millero 1987]. L&IL A,A(sample) = A.A(indi cator) + A.A(blank) calculations: 444 616 750 A (sample) 0.8344 0 .5000 0 .0704 A (blank) 0 .0000 0.0090 0.0700 A (blank corrected) 0.8344 0.4910 0.0004 A (baseline shift corrected) 0 .8340 0.4906 0.0000 A (indicator ) 0.8340 0.4906 (Note that careful cleaning of cell windows will generally reduce apparent baseline shifts to negligible levels.) III. Temperature (t) is 24.6. IV. R(t) = [0.4906/0.8340] = 0 5882s V. R(25) = R(t) { 1 + 0.00907(24.6 25)} = 0 .5861t6 VI. S(a) = 34.4959 [density = 1.022962 g/mL] [Note: For this step the titrant is assumed to be pure water, which at 25 C has a density of 0.997048 g/mL ] VII. log 1 T(s) = 4.2712o VIII. log = 4.4169o

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Appendix 2 (Continued) 114 IX pH = 3.83392 thus [H+ ]-1 = 6,822.13 m-1 X ST = 0 028833 m and FT = 0.0000715 m XI. 1 = 12.526 m-1 for S(a) = 34.495g XII. Q = 1.7168 x10-3 thus -log (1 Q) = 0.000746 XIII. pHT = 3.68897 whereby [H+]T = 2.0466 x10-4m [equivalent to [H+]T = 1.9756 x10-4 mol/kg(sw ) l XIV. IT = 2.62 x106m [equivalent to IT = 2 .53 x10-6 mol/kg(sw)l and [HI-] = 2 .0g x10-6m [equivalent to [HI-] = 2.01 x10 6 mol/kg(sw)l Therefore, XV. rna V a = 267 625 ).!mol, V sa([H+]T + [ID-]) = 20.6go ).!mol; and (TA)s = 2413 1 Jlmol/kg(sw)

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APPENDIX 3 SAS program FINAL (used for the salt solution titration data sets) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30 31. 32. 33 34. 35. 3 6 37. 38. 39 40. 41. 42. 43. 44. 45. 46. 47. 48 49 50. 51. 52. 53. 54. I I JOB IISTEP1 EXEC SAS IISASGREEN DO DSN=DKFADAA.BCG(017 N),DISP=SHR IISYSIN DO ****************** PROGRAM FINAL **************; DATA; I NF I LE SASGREEN; INPUT HMOLAR L4 L6; PK2 = 4.4306; *H=HMOLARI0. 9772; *FOR USE WITH DATA SET J07K; H=HMOLARI0.9844; *FOR USE WITH DATA SET D17N AND J14N; *H=HMOLARI0.9867; *FOR USE WITH DATA SET J14MG; R=L61L4; PHT=-LOG10(H); *IT=1.01E-6; *FOR DSN N22K AND N22N; *#*#*REMOVE EITHER ASTERIX ABOVE OR THE ONE BELOW DEPENDING ON DSN; lT=2.69E; *FOR DSN D17N,J07K,J14MG,J14N; IB2 = 10**PK2*CALCULATED FROM PK2; E1=0. 001310 ; I E2=2. 31477; E3=0. 12988; AT=LOG10((R-E1)1(E2-(R*E3))); PHF = PK2 + AT; FH = 10**(-PHF); PRO C NLIN METHOD=MAROUARDT MAXITER=300 PLOT; PARAMETERS DT=0.000008, DB1=16161; BOUNDS 0 .0001 >DT> 0.0 1E9 >DB1> 1E3; MODEL PHT = PK2 +AT LOG10 ( 1 + (!B2*!T) + (OBl *DT) -((182**2)*11) I (IB2+(11FH)) DER.DT (0.43429448 2 ) I ) ) ; -((DB1**2)*0T) I (DB1 +(11FH)) ) ; + (IB2*1T) + (DT*DB1> -((182**2)* 11) I (!82+(11FH)) -((081**2)* 0T) I (081+(1 1FH)) 081 (081**2) I (081 +(11FH)) DER.D81 (0.43429 4482) I 1 + (182*1Tl (081*01) -((! 82**2)*!T) I ( !82+(11FH)) ); -((081**2)* 01) I (081 + (11FH)) DT ((((081 + (11FH))*2*DT*D81) (081**2)*01) I (081+(i/FH))**2) OUTPUT OUT=OATA PREDICTED=PRE RESIDUAL=RES; PROC PRINT; II 115

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Appendix 3 (Continued) 116 The following data from salt solution titrations are used by the SAS program FINAL gtven above. Data set D17N Data set J07K Point# [H+] 444A 616A Point# [H+] 444A 616A 1. 2.917E-5 0.2283 0.6576 1. 3.418E-5 0.2471 0.5799 2. 3.583E-5 0.2519 0 .5950 2. 4.083E-5 0.2654 0.5316 3. 4.248E 0.2705 0.5447 3. 4.748E-5 0.2811 0.4890 4. 4.914E-5 0.2868 0.5017 4. 5.412E 0.2946 0.4534 5. 5.579E 0.3009 0.4639 5. 6.077E 0.3064 0.4223 6. 6.245E-5 0.3132 0.4315 6. 6.742E-5 0.3163 0 .3953 7 6.910E-5 0.3239 0 .4031 7. 7.406E-5 0.3252 0.3720 8. 7.908E-5 0.3372 0.3670 8. 8.071E-5 0.3332 0.3506 9. 8.905E-5 0.3488 0.3364 9. 8.735E-5 0.3403 0.3313 10. 9.903E-5 0.3583 0.3111 10. 9.399E 0.3476 0.3146 11. 1.123E-4 0.3689 0.2822 11. 1.040E 0.3551 0.2922 12. 1.289E-4 0.3800 0.2532 12. 1.139E 0 .3623 0 2727 13. 1.455E-4 0.3888 0 .2294 13. 1.239E-4 0.3688 0.2557 14. 1.621E-4 0.3963 0.2094 14. 1.338E-4 0.3742 0.2408 15. 1. 953E-4 0.4078 0.1783 15. 1.471E-4 0.3810 0.2233 16. 2.285E-4 0.4162 0.1562 16. 1.604E-4 0.3866 0.2080 17. 2.616E-4 0.4227 0.1384 17. 1. 769E 0.3927 0 .1916 18. 2.948E-4 0.4279 0.1246 18. 1.935E-4 0.3979 0 1777 19. 2.101E-4 0.4024 0.1658 20. 2.267E-4 0.4063 0.1550 21. 2.598E-4 0.4127 0.1380 22. 2.929E-4 0.4178 0.1239 Data set J14N Data set J14Mg Point# [H+] 444A 616A Point# [H+] 444A 616A 1. 4.571E-5 0.2493 0.5802 1. 3.308E-5 0 .2343 0.6133 2. 5.236E-5 0.2680 0.5314 2 3.973E-5 0.2543 0.5609 3 5.901E-5 0.2837 0.4890 3 4.638E-5 0 .2706 0 .5159 4. 6.566E-5 0.2975 0.4524 4. 5.302E-5 0.2850 0 .4781 5. 7.230E-5 0.3096 0.4207 5 5.967E 5 0 .2979 0.4441 6. 7 895E-5 0.3195 0.3946 6. 6.632E-5 0.3088 0.4142 7. 8 560E-5 0.3286 0 3708 7. 7.296E-5 0.3184 0 .3883 8. 9.224E-5 0.3363 0.3500 8. 7.960E-5 0.3270 0 .3663 9. 9.889E-5 0.3440 0 .3304 9. 8.625E-5 0.3344 0 3460 10. 1.055E 0.3504 0.3132 10. 9.289E-5 0.3414 0.3278 11. 1. 122E 0.3560 0.2978 11. 9.953E-5 0.3474 0.3113 12. 1.255E 0.3660 0.2714 12. 1.062E 0.3530 0. 2 9 5 9 13. 1.387E-4 0.3744 0.2490 13. 1 161E-4 0.360 4 0.2760 14. 1 520E-4 0.3812 0.2301 14. 1.261E-4 0.3668 0.2594 15. 1.653E-4 0.3873 0.2142 15. 1.360E-4 0.3725 0.2439 16. 1. 786E-4 0.3925 0.2002 16. 1.526E 4 0.3808 0.2223 17. 1.951E 0.3983 0.1852 17. 1.692E-4 0 .3875 0.2037 18. 2.117E 0.4030 0.1722 18. 1.858E-4 0.3933 0 .1882 19. 2.283E 0.4072 0.1611 19. 2.023E-4 0.3984 0.1749 20. 2.448E 0.4108 0.1512 20. 2.189E 0.4026 0 .1634 21. 2.780E 4 0.4170 0.1348 21. 2.520E4 0.4094 0.1443 22. 3.110E-4 0.4217 0.1216 22. 2.851E4 0.4149 0 .1293

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Appendix 3 (Continued) SAS program BCGSWFIN (used with sea water data sets) 1. 2 3. 4. 5. 6. 8 9. 10. 11 12. 13. 14. 15. 16. 17. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38 39. 4 0 41. 42. 4 3 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. II JOB IISTEP1 EXEC SAS IISASGREEN DO DSN=DKFADAA.BCG(D08),DISP=SHR IISY SIN DO **************************** PROGRAM DATA; INFILE SASGREEN; ******************* INPUT HMOLAR L4 L6 TVOL; H=HMOLARI0.987; R=L61L4; *VC=149.9211TVOL; *FOR USE DSN N27; VC=149.9 6 5/TVOL; *FOR USE DSN 008 AND 013; ST=VC* 2.927E-2; FT=VC*7.26E-5; IT=VC*2.02 E-6; *FOR USE DSN N 27 OR 008; *IT = VC*2.69E-6; *FOR USE DSN 0 13; E1=0.00131; E2=2.31477; E3=0. 12988; PK2=4.4166 ; FB1=418. 1; IB2=10**PK2 PHT=LOG 10( io; AT= LOG10((R-E1)1(E2-E3*R)); PHF=PK2+AT; FH=10**(-P HF); PROC NLIN METHOD=MAROUARDT MAXITER=300 PLOT; PARAMETERS SB1=1 2,DB1=94649,DT=2 .6E-5; BOUNDS SB1> 0.0, DB1 > 0.0, DT > 0.0; MODEL PHT = PK2 + AT LOG10 ( 1 +{SB1*ST)+(FB1*FT)+(DB1*DT)+{IB2*1T) -(((SB1**2)*ST) I (S81 + ( 11FH))) -(((FB1**2)*FT) I (FB1 + (11FH))) -{((DB1**2)*0T) I (0B1 + (11FH))) -(((182**2)IT) I (182 + (11 FH))) ); DER.SB1 (0.434294482) I ( 1 + (SB1*ST) + (FB1*FT)+(08 1*DT)+{IB2*1T) -(((SB1**2)*ST) I (S81 + (11FH))) -(((FB1**2)*FT) I (F81 + (11FH))) (((DB1**2)*0T) I (0B1 + (11FH))) -(((1B2**2)*1T) I (IB2 + (11FH))) ) ST -((((S81+(1 1FH))*2*S B1*ST) -(S81 **2 )*ST) I (SB1+(11FH))**2 ) ); D ER.D81 -(0. 434294482) I 1 + (SB1*ST) + (FB1*FT)+(D81*DT)+(IB2*1T) -(((SB1 **2 ) *ST) I (58 1 + (11F H))) -(((FB1**2) *FT) I (F81 + (11FH))) -(((081**2) 0T) I (081 + ( 1 1 F H))) -(((1B2**2) JT) I (182 + (11FH))) ) DT ((((081+(1/FH))*2*D81*D T ) (081**2)*0T) I (081+{11FH))**2) ); DER.DT -(0. 434294482) I 1 + (S81*ST) + (FB1*FT)+(D81*DT) + ( I 82*1T) -(((S81**2)*ST) I (S81 + (11FH))) -(((FB1**2)*FT) I (FB1 + ( 1 1FH))) -(((081 **2)*0T) I (081 + (11FH)) ) -(((IB2 **2)*JT) I (1B2 + ( 1 1FH))) DB1 ((0B1**2) I (081+(11FH))) >; OUTPUT OUT=DATA PREDICTED=PRE RESJDUAL=RES; PROC PRINT; II 1 1 7

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Appendix 3 (Continued) 118 The following data from sea water titrations are used by the SAS program "BCGSWFIN" gtven above. Data set RD0 8 Point# [H+] 444A 616A Volume(mL) 1. 3.316E-5 0.1456 0.5730 150.52 2. 3.980E-5 0.161 2 0.5322 150.53 3. 4.644E-5 0.1750 0 4956 150.54 4. 5.308E-5 0 .1872 0.4638 150.55 5. 5.972E-5 0 .1981 0 .4347 150.56 6. 6.635E-5 0 .2077 0 4095 150.57 7 7.299E-5 0.2167 0.385 9 150.58 8 7 .963E -5 0.2243 0. 3655 150.59 9. 8.958E-5 0.2346 0.3385 150.605 10. 9 .953E-5 0.2434 0 3150 150.62 11 1.128E-4 0.2535 0 .28 82 150.64 12. 1. 261E -4 0 2619 0 .2655 150 .66 13. 1.459E-4 0 2723 0.2375 150.69 14. 1 .625E-4 0 2797 0.2184 150 .715 15. 1.791E-4 0.2857 0.2018 150.74 16. 2.122E-4 0 .2955 0.1757 150 .79 17. 2.452E-4 0.3030 0.1555 150.84 18. 2.783E-4 0.3091 0 .1394 150.89 Data set RD13 Po i nt# [H+] 444A 616A Volume(mL) 1. 3.325E -5 0.1849 0.7735 150 .585 2. 3 989E-5 0.2053 0.7186 150.595 3. 4 652E-5 0 .2240 0.6699 150 605 4. 5.316E-5 0.2408 0.6250 150.615 5. 5.980E-5 0 .2554 0.5859 150.625 6 6.643E-5 0.2683 0.5513 150.635 7. 7 306E-5 0 .2800 0 5203 150.645 8. 7.970E-5 0.2906 0.4923 150.655 9. 8.633E-5 0.3000 0.4673 150 .665 10. 9.495E-5 0 3110 0.4378 150.678 11. 1. 029E-4 0 .3201 0.4136 150.69 12. 1.128E-4 0.3299 0.3870 150.705 13. 1.235E-4 0.3392 0 3622 150.721 14. 1.394E-4 0.3512 0.3300 150.745 15. 1 559E-4 0 3619 0.3020 150. 77 16. 1. 725E-4 0.3704 0.2785 150.795 17. 1.890E-4 0 3780 0 .25 83 150.820 18. 2.056E-4 0.3845 0 .2408 150.845 19. 2 221E-4 0.3901 0 .2255 1 50.87 20. 2.386E-4 0 3949 0.2119 150.895 21. 2.71 7E-4 0.4034 0.1893 150.945 22. 3 047E-4 0.4101 0.1709 150.995 Data set RN27 Point# [H+] 444A 6 1 6 A Volume(mL) 1 4.302E-5 0.1706 0.5266 150.441 2. 4.967E-5 0.1830 0.4916 150.451 3. 5.631E-5 0.1947 0.4605 150.461 4. 6.295E-5 0 2050 0.4324 150 .471 5 6_959E-5 0.2146 0.4074 150.481 6. 7.955E-5 0.2268 0.3747 150.496 7. 8.619E5 0.2339 0.3560 150.506 8. 9.61 5E-5 0 2433 0.3304 150.521 9 1.061E-4 0 2517 0.3081 150.536 10. 1.161E-4 0 2590 0 2886 150.551 11. 1.227E-4 0 2630 0. 2771 1 50.561 1 2 1. 293E -4 0.2670 0.2664 150.571 13. 1.459E-4 0.2759 0.2425 150.596 14. 1 .625E4 0.2833 0.2231 150.621 15. 1. 956E-4 0.2949 0.1916 150.671 16. 2.287E-4 0.3036 0 1676 150 .721 17. 2 618E-4 0.3105 0.1493 150.771 18. 2.949E-4 0.3160 0.1343 150.821


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