Two-method verification of hydrogen peroxide determinations in

May 12, 1986 - R. F.; Ed.; Marcel Dekker: New York, 1978; Part 2, Chapter 19. (3) Sternberg, J. C. Clin.Chem. (Winston-Salem, N.C.) 1977, 23,. 1456-14...
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Anal. Chem. 1986, 58, 2312-2315

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potential applicability of these methods to turbidimetric data obtained with multichannel instruments such as centrifugal mixing systems (19).

(11) Tengerdy, R. P. J. Immunol. 1987, 99, 126-132. (12) Marrack, J. R.; Richards, C. B. Immunology 1971, 20, 1019-1039. (13) Killingsworth, L. M.; Savory, J. Clin. Chem. (Winston-Salem, N.C.) 1973, 19, 403-407. (14) Savory, J.; Buffone, G.; Reich, R. din. Chem. (Winston-Salem, N.C.) 1974, 20, 1071-1075. (15) Whicher, J. T.; Perry, D. E. In Practical Immunoassay, The State of the Art; Clinical Biochemistry Series; Marcel Dekker: New York, 1984; Vol. 14, Chapter 6. (16) Hellsing, K. Automated Immunoanalysis; Richie, R. F., Ed.; Mercel Dekker: New York, 1978; Part 1, Chapter 3. (17) Hudson, G. A.; Ritchie, R. F.; Haddow, J. E. din. Chem. (Winston-Salem, N.C.) 1981, 27, 1838-1844. (18) Skoug, J. W.; Weiser, W. E.; Cyliax, I.; Pardue, H. L. Trends Anal. Chem., In press. (19) Savitzky, A.; Golay, M. J. E. Anal. Chem. 1964, 36, 1627-1639.

LITERATURE CITED (1) Buff one, G. J.; Savory, J.; Hermans, J. Clin. Chem. (Winston-Salem, N.C.) 1975, 21, 1735-1746. (2) Anderson, R. J.; Sternberg, J. C. Automated Immunoanalysis; Richie, R. F.; Ed.; Marcel Dekker: New York, 1978; Part 2, Chapter 19. (3) Sternberg, J. C. Clin. Chem. (Winston-Salem, N.C.) 1977, 23,

1456-1464.

(4) Tiffany, T. O.; Parella, J. M.; Johnson, W. F.; Burtis, C. A. Clin. Chem.

(Winston-Salem, N.C.) 1974, 20, 1055-1061.

(5) Wu, J. W.; Bunyagid), C.; Et al. Clin. Chem. (Winston-Salem, N.C.)

1983, 29, 1540-1542.

(6) Lin, J. D.; Pardue, H. L. Clin. Chem. (Winston-Salem, N.C.) 1982,

28, 2081-2087.

(7) Pardue, H. L.

2189-201.

Received for review January 28,1986. Accepted May 12,1986.

Clin. Chem. (Winston-Salem, N.C.) 1977, 23,

This work was supported by Grant No. CHE 8319014 from the National Science Foundation. John W. Skoug expresses gratitude to the American Chemical Society—Division of Analytical Chemistry for a summer fellowship.

(8) Mieling, F. E.; Pardue, H. L. Anal. Chem. 1978, 50, 1611-1618. (9) Harner, R. S.; Pardue, H. L. Anal. Chim. Acta 1981, 127, 23-38. (10) Hamilton, S. D.; Pardue, H. L. din. Chem. (Winston-Salem, N.C.)

Downloaded via IOWA STATE UNIV on January 29, 2019 at 07:27:22 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

1982, 28, 2359-2365.

Two-Method Verification of Hydrogen Peroxide Determinations in Natural Waters R. J. Kieber* and G. R. Helz

Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742

limits without interference from the numerous other oxidizing substances found in natural waters. In choosing to develop an iodometric method rather than one of the alternatives, we were influenced by the fact that has been achievement of sub-micromolar detection

An Iodometric titration method Is Investigated for verifying H202 determinations In natural water matrices. Hydrogen peroxide oxidizes Iodide to Iodine at pH 4 in the presence of ( 4)ß 7 24·4 20. The I2 that is generated reacts with an added spike of phenylarslne oxide, the excess of which is titrated with a standardized Iodine tltrant to an amperometrically determined end point. The difference between titrations with and without the enzyme catalase Is proportional to the H202 concentration. The detection limit Is estimated to be 0.02 µ . A previously described Independent fluorometric method Is In excellent agreement with this method when applied to fresh and saline natural waters containing 0.05-5.00 µ H202. Demonstration of such agreement can be used for verification purposes In the absence of certified standards.

iodometry is usually the ultimate calibration method for H202 standards in the laboratory (16-18). Furthermore, the equipment needed is reasonably portable and also often available in water analysis laboratories because of its use in the determination of chlorine. Of the methods cited above, the spectrophotometric and fluorometric methods are not independent of one another, since both depend on the use of a peroxidase enzyme to catalyze a reaction between H202 and a chromophore or fluorophore. Thus, they cannot be used for cross verification. While the chemiluminescence methods are independent of the spectrofluorometric methods, they require special equipment and are prone to interferences.

EXPERIMENTAL SECTION General. Iodide can be oxidized quantitatively to iodine by aqueous hydrogen peroxide in acidic solutions (17)

For unstable analytes in natural waters, verification of analytical results is not easily performed in the usual way, through use of round robins or certified reference materials. Verification is therefore most readily achieved by demonstrating in each laboratory that consistent analytical results can be obtained with two completely independent methods. In this paper we report the development of an iodometric procedure for determining H202 at concentrations found in natural waters and the use of this method to confirm results obtained by a fluorometric method developed by others (1-3). Hydrogen peroxide is a byproduct of atmospheric and aquatic photochemistry. Its measurement in natural waters has attracted interest in part because of its recently recognized role in converting S02 to H2S04 in aqueous aerosols (4, 5). A variety of analytical approaches are available for H202, including chemiluminescence methods (6-11), spectrophotometric methods (12,13), and fluorometric methods (1-3,14, 15). A major concern in the development of these methods 0003-2700/86/0358-2312$01.50/0

2H+ + H202 + 2D

At pH



I2 +

2H20

(1)

interference. To avoid this, we buffer the solution at pH 4. However, at pH 4 reaction 1 needs the assistance of a molybdate catalyst (19, 20). An excess of phenylarsine oxide is added to the sample to consume I2 as it is generated. The analytical result is obtained by titrating the remaining phenylarsine oxide to an amperometric end point with I2 2 or

lower, oxygen also oxidizes T, creating

an

O

2H20 + I2 +

As

2

+ 2H+

+

As-OH OH

(2)

©

1986 American Chemical Society

ANALYTICAL CHEMISTRY, VOL. 58, NO. 11, SEPTEMBER 1986

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Phenylarsine oxide was chosen as the iodine scavenger for several reasons: (a) it is readily available commercially; (b) a standardized solution is stable over long periods of time; (c) it reacts extremely rapidly with aqueous halogens (21) and thus should be able to compete effectively with any iodinereactive substances in the sample. Because a variety of naturally occurring oxidants are capable of converting aqueous iodide to iodine, it is necessary to use the enzyme catalase to gain specificity for H202. The sample is split and half is treated with catalase. Both are then titrated and the concentration of hydrogen peroxide is de-

termined by difference. Several assumptions are made in this procedure. First, any iodine demand in the sample (exerted by natural reducing agents after the excess PAO is consumed) is the same in the untreated and catalase-treated aliquots of the same sample. This was found to be true in the samples we studied provided the catalase concentration was kept at moderate levels (catalase itself consumes some I2). Second, the iodine generated by the oxidants in solution is assumed to react exclusively with the excess phenylarsine oxide spike. Finally, it must be assumed that no loss of phenylarsine oxide occurs except by reaction with iodine during the analysis. Tests conducted during this study as well as past experience in our laboratory indicate that phenylarsine oxide itself is quite stable in natural

waters.

Reagents. Water from a deionization/activated carbon absorption system (Milli-Q System, Millipore Corp.) was further purified by a slow redistillation from potassium permanganate. It was stored in either amber glass bottles or Nalgene polyethylene bottles for periods up to several weeks. A 10"3 M H202 solution prepared in the purified water showed no change in peroxide concentration over the course of 1 week. All chemicals and reagents were used without additional purification. A saturated aqueous solution of (NH4)6Mo7024·4 20 (Fisher Certified ACS) served as the molybdate HI solution was prepared by dissolving 0.83 catalyst. A 0.1 g of Baker Analyzed reagent grade HI in 50 mL of the purified water. It was prepared fresh daily and stored in a 50-mL amber glass bottle. The 5.64 X 10~3 N phenylarsine oxide solution was purchased from Hach Co. and was standardized with iodate upon arrival. Bovine liver catalase (2800 units/mg solid), horseradish peroxidase (type II, 200 units/mg solid) and scopoletin (6-methyl-7-hydroxyl-l,2-benzopyrone) were all obtained from Sigma Chemical Co. The catalase stock solution (1.0 mg/mL) was made fresh every 7-10 days. The 4 mg/mL horseradish peroxidase stock solution used in the fluorometric procedure was buffered with 0.01 M phosphate at pH 7 and contained 1 X 10"3 M phenol. The iodine used as a titrant was made from a dilution of a 0.1 N I2 stock solution. It was stored in the Brinkmann amber glass titrating apparatus and was standardized several times daily against the phenylarsine oxide. Hydrogen peroxide, 30%, used in the preparation of H202 stock solutions and standards was obtained from Baker Chemical Co. (Reagent Grade). Equipment. Amperometric titrations were carried out with a Brinkmann Potentiograph, Model E436. The instrument is equipped with a stationary platinum anode and a rotating spiral platinum cathode. The potential between the electrodes is kept at a constant 200 mV. Fluorescence measurements were made on a Turner Designs Model 10 fluorometer with an excitation wavelength of 365 nm and an emission wavelength of 490 nm. Iodometric Procedure. Add 1 mL of acetate buffer (0.1 M, pH 4) to 100 mL of sample. Next add a known spike of phenylarsine oxide solution. The exact amount of this reagent will depend on the concentration of hydrogen peroxide in the

TIME

(minutes)

Figure 1. Decay of hydrogen peroxide in a 20-mL natural water sample with time in the presence of 5 µ of 1.0 mg/mL catalase.

sample. Preliminary experiments may be needed to find the optimum amount. Next add 3 mL of the freshly prepared 0.1 KI along with 100 µL of the saturated Mo catalyst solution. The sample is stirred for 15 min during which time iodine is generated by hydrogen peroxide (eq 1) and possibly by other oxidants in the solution. The generated I2 is destroyed by the added phenylarsine oxide, the excess of which is subsequently titrated with the standardized iodine to an amperometrically determined end point. A second titration is performed in an analogous manner except that the hydrogen peroxide in the sample is first destroyed by the enzyme catalase. This is accomplished by adding 25 juL of a 1.0 mg/mL catalase solution per 100 mL of sample and stirring for 25 min. Fluorometric Procedure. One hundred microliters of pH 7 phosphate buffer (0.1 M) is added to 20 mL of sample and inserted into the fluorometer. The instrument is set to 0%

transmission. To this a known quantity of the fluorophore scopoletin (typically 5 X 10""5 M) is added and the instrument scale is set to its maximum. The hydrogen peroxide in the sample oxidizes the scopoletin upon addition of 20 /íL of the horseradish peroxidase stock solution, resulting in an immediate decrease in fluorescence. The hydrogen peroxide concentration is determined from the difference in fluorescence before and after addition of the catalyst. Calibration curves are obtained by recording the decrease in fluorescence upon addition of a H202 stock solution to the sample. Reagents are mixed continuously by means of a magnetic stirring device located at the bottom of the fluorescence cell. The reported detection limit is 2 X 1( 9 M hydrogen peroxide and the precision is 2% (22).

RESULTS Conditions for the Iodometric Method. Experimental The amount of catalase needed to completely destroy the ambient hydrogen peroxide is sample dependent. It should be sufficient to destroy all the hydrogen peroxide in a reasonable amount of time, yet exert no iodine demand. The catalase concentration chosen was based on the results of the following two experiments. The first was designed to determine the time required for the enzyme to destroy all the hydrogen peroxide in a natural water matrix at a fairly high H202 concentration. Four liters of water from Paint Branch (a stream on the University of Maryland campus) was collected in an amber glass bottle. This sample was brought back to the lab and H202 was added until the final concentration exceeded 8 X 10™7 M. Five micrograms of catalase was added to a 20-mL aliquot of the sample and the hydrogen peroxide concentration was monitored by the fluorescence decay technique. The decay of the H202 (indicated by a decreasing fluorescence change) is presented in Figure 1. The fluorescence change recorded at time = 0 reflects the magnitude of

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·

ANALYTICAL CHEMISTRY, VOL. 58, NO. 11, SEPTEMBER 1986 t -

SCALE

0.0I

MICROEQUIVALENTS

o: CE

3 u

Q O

0

20

100

CE

200

300

pL CATALASE STOCK SOLUTION Ld

l2

TITRANT

VOLUME

Figure 2. Recorder traces of electrode current vs. titrant volume for five samples containing different amounts of catalase stock solution (volumes shown were added to 100 mL of distilled water). The end point is reached when there is an abrupt rise In current. This experiment demonstrates that catalase exerts I2 demand.

Table I. Recovery of Hydrogen Peroxide in Permanganate Distilled Water and Paint Branch River Water by Two Independent Methods0 H202 added

H202 found by fluorescence

H202 found iodometrically

3.1 0.31

3.0 0.31

B. Paint Branch Water 2.7 0.31

2.5 0.32

both the iodine and fluorescence methods. The comparisons presented in Table IB. Again, the spike was quantatively recovered, within error, by the I2 analysis. Also, within the normal limits of error, the fluorescence and iodine methods produced analytically equivalent hydrogen peroxide results. Organic peroxides potentially interfere in both methods employed in this study. The horseradish peroxidase enzyme used in the fluorescence method reacts with low molecular weight organic peroxides (3) as does the enzyme catalase used in the iodometric technique (23). However, it is known that catalase decomposes hydrogen peroxide more readily than organic peroxides (23). This preferential H202 degradation was used to evaluate the possibility of interference caused by organic peroxides. Several liters of Patuxent River water were collected at Benedict, MD, and were refrigerated. On the next clear day, two aliquots were withdrawn and placed in 500-mL quartz round-bottom flasks. These were placed on the building roof for a total of 3 h of sunlight exposure (10.00 a.m. to 1.00 p.m.), during which time peroxides were generated photochemically. A third aliquot was kept in the dark. The irradiated samples were taken back to our laboratory and the peroxide level was determined by the fluorescence technique to be 3.8 X "7 M. Hydrogen peroxide was then added to the nonirradiated flask to give a final level of 3.8 X 7 M H202. Sixty microliters of catalase (0.5 mg/mL) was added to one of the irradiated flasks and to the H202 spiked flask. The decay in the peroxide signal was followed in all three samples by the fluorescence technique. Figure 3 shows the results. The rate of peroxide decay is very similar in the sample containing authentic H202 and in the sample containing photochemically generated peroxides. The indicates that very little, if any, organic peroxide was contributing to the analytical results in the photolyzed sample. This result is in agreement with others who found in a variety of natural waters that the organic peroxide content was negligible compared to that of H202 (3, 24). Field Measurements. The concentration of hydrogen peroxide in Paint Branch water was determined by the iodometric and fluorometric methods throughout the summer of 1985. Surface samples were collected by immersion of 4-L amber glass bottle. Analyses were begun within 5 min of sampling. The results are presented in Figure 4. In almost all cases the disparity between the fluorescence and iodine methods is less than a few percent (even at 10“8 M H202), well within the analytical uncertainty. Hydrogen peroxide analyses were also conducted on September 17 and 18,1985, on the Patuxent River at the Benedict are

A. Distilled Water 3.1 0.31

Figure 3. Decay of hydrogen peroxide, as measured by fluorescence change, with time In Patuxent River water. The upper curve demonstrates that the scopoletin reactive oxidant generated by solar photolysis is moderately stable in the absence of added catalase. The identical decay rates of the solar photolysis oxidant and H202 in the presence of catalase (lower curves) suggests that the photolysis product is indeed H202.

2.6 0.31

Concentrations in micromolar units.

the signal before catalase was added to the natural water. After six half-lives (the decay being approximately first order) or 25 min the hydrogen peroxide signal in the spiked Paint Branch water had fallen to an undetectably low level. Figure 2 is a presentation of the results of some tests to determine the iodine demand of catalase. Various concentrations (0, 0.2, 1, 2, 3 mg/L) of the enzyme were added to permanganate-distilled water and then titrated with iodine. Appearance of free iodine in the solution at the titration end point is marked by a sudden rise in electrode current. Dead time, related to the rate of mixing of I2 in the titration vessel, results in a finite volume of titrant being added before a current response is observed even in the absence of ^-consuming components. As seen in Figure 2, a 20-mL addition of catalase, representing a concentration of 0.2 mg/L, produces an iodine demand too small to be distinguished from zero. Higher concentrations of catalase, however, produce a demand that could cause significant error in the determination of H202 below 10'7 M. Based on the results presented in Figures 1 and 2, we chose a catalase dose of 0.25 mg/L and a reaction time of 25 min for subsequent work. To test recovery, a known quantity of hydrogen peroxide was added to 1-L of the permanganate-distilled water. This sample was analyzed by both the fluorescence decay and the iodine techniques. The amount of hydrogen peroxide found by each analysis and the added H202 level are presented in Table IA. The I2 method was able to recover quantitatively the hydrogen peroxide spike at micromolar and sub-micromolar levels. It also produced results that were identical, within analytical precision, with the fluorescence decay technique. In a similar experiment, river water from Paint Branch was spiked with a known quantity of hydrogen peroxide. The concentration of H202 in the sample resulting from the spike exceeded, by over an order of magnitude, the ambient concentration of the oxidant. The dosed water was analyzed by

ANALYTICAL CHEMISTRY, VOL. 58, NO. 11, SEPTEMBER 1986

Figure 4. Intercomparison between the Iodometric method and the fluorescence decay method on Paint Branch water collected throughout the summer of 1985. The line represents perfect agreement between results, not a statistical fit to the data.

Table II. Concentration of Hydrogen Peroxide (Micromolar) Found in Patuxent Estuarine Water by the Iodine and Fluorescence Methods fluorescence method

0.056 0.086 0.050

0.054 0.084 0.075

B. Variably Spiked Samples Collected in April, 1986 0.058 0.089 0.099 0.102 0.107 0.150 0.180 0.235 0.590

0.060 0.094 0.096 0.110 0.115 0.147 0.181 0.233 0.572 0

Fluorescence analyses performed by Philip Kijak.

Estuarine Laboratory. This is a saline estuarine water in contrast to the fresh samples from Paint Branch. The hydrogen peroxide values obtained are presented in Table IIA. In the first two cases the agreement between the results obtained by the iodine and fluorescence methods is excellent. The reasons behind the relatively poor agreement in the last reading are not known, but may involve operator error. Additional saline samples were collected at Benedict, MD, in April of 1986. Each was refrigerated in the dark until use. In order to obtain a measurable signal (the ambient H202 had decayed to an undetectably low level between the time of collection and analysis) stock hydrogen peroxide was added to each sample prior to analysis. The H202 determined in these Benedict samples are presented in Table IIB. The agreement between the results was again well within analytical error, as was the case with the fresh Paint Branch water. Because the H202 decay rate was greater in the saline samples than in the freshwater samples, special care had to be taken to make the two measurements at the same time after the H202 spike had been added.

DISCUSSION The precision of a single iodometric titration is controlled by the precision of three measurements, the volume of sample, the volume of phenylarsine oxide added, and the volume of I2 titrant. With use of standard glassware, the uncertainty in the first two measurements can be ±1%. The precision of the third measurement is instrumentation dependent. For

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our system, we estimate it to be ±0.005 gequiv. However, three titrations are required for a given H202 determination: one to calibrate the I2 titrant against phenylarsine oxide and two to quantify the oxidants in the sample before and after addition of the catalase. The total uncertainty is consequently larger than the uncertainty of a single titration. At low concentrations, the determination of titrant volume will control the uncertainty so the total uncertainty in a H202 determination will be about ±0.015 ^equiv. With a conventional definition of detection limit as three times the uncertainty, this limit would be 0.045 /tequiv or 0.02 µ . The key to use of the iodometric method for H202 is the availability of sensitive instrumentation for determining I2 or phenylarsine oxide. We used a research grade amperometric titrator; however, other possibilities exist. Phenylarsine oxide may be determined directly by polarography (25). Alternatively, the end point of an iodometric titration can be determined with good sensitivity by potentiometric (26) and spectrophotometric (27) methods. Furthermore, inexpensive, portable amperometric titators are available which have been shown to yield very good results down to about 0.8 µ (28). This versatility with regard to instrumentation requirements makes the iodometric technique attractive.

iodine method

A. Natural Concentrations (September 1985)°

«

ACKNOWLEDGMENT The authors are grateful for advice and support recieved from William Barger at Naval Research Laboratory, James Sanders at the Philadelphia Acadamy of Sciences, and Rod Zika at the University of Miami. Field assistance from Philip Kijak is also greatly appreciated.

Registry No. H202, 7722-84-1; H20, 7732-18-5. LITERATURE CITED (1) Perschke, H.; Broda, E. Nature (London) 1961, 190, 257-258. (2) Van Baalen, C.; Marler, J. E. Nature (London) 1966, 211, 951. (3) Zika, R. G.; Moffett, J. W.; Petasne, R. G.; Cooper, W. J.; Saltzman, E. S. Geochim. Cosmochim. Acta 1985, 49, 1173-1184. (4) Penkett, S. A.; Jones, B. M.; Brice, K. A.; Eggleton, A. E. Atmos. Environ. 1979, 13, 123-137. (5) Calvert, J. G.; Lazrus, A.; Kok, G. L; Heikes, B. G.; Walega, J. G.; Lind, J.; Cantrell, C. A. Nature (London) 1985, 317(5), 27-35. (8) Slnel'nikov, V. Ye. J. Hydrobiol. 1971, 7, 96-99. (7) Kok, G. L.; Holler, T. P.; Lopez, . B.; Nachtrleb, . A.; Yuan, M. Environ. Sci. Technol. 1978, 12, 1072-1076. (8) Kok, G. L. Atmos. Environ. 1980, 14, 653-655. (9) Das, T. N.; Moorthy, P. N.; Rao, K. N. Atmos. Environ. 1983, 17,

79-82.

(10) Ibusuki, T. Atmos. Environ. 1983, 17, 393-396. (11) Neftel, A.; Jacob, P.; Klockow, D. Nature (London) 1984, 311, 43-45. (12) Mottola, . A.; Simpson, B. E.; Gorin, G. Anal. Chem. 1970, 42,

410-411.

(13) Draper, W. M.; Crosby, D. G. Arch. Environ. Contam. Toxicol. 1983, 12, 121-126. (14) Lazrus, A. L; Kok, G. L; Gltlin, S. N.; Lind, J. A. Anal. Chem. 1985,

57, 917-922.

(15) Helz, G. R.; Kleber, R. J. Water Chlorination Lewis Publishers: Chelsea, MI, 1985; Vol. 5, pp 1033-1040. (16) Rlcciuti, C.; Coleman, J. E.; Wlllits, C. O. Anal. Chem. 1955, 27, ·,

405-407.

(17) Kolthoff, I. M.; Belcher, R. Volumetric Analysis·, Interscience Publishers: New York, 1957. (18) Johnson, R. M.; Slddlql, I. W. The Determination of Organic Peroxides Pergammon Press: London, 1970. (19) Smith, R. H.; Kllford, J. Int. J. Chem. Kinet. 1978, 8, 1-10. (20) Kosak-Channing, L. F. Ph.D. Thesis, Chemistry Department, University of Maryland, 1981. (21) Jaworske, D. A.; Helz, G. R. Int. J. Environ. Anal. Chem. 1985, 19, ·,

189-202.

(22) Zika, R. G.; Saltzman, E. S.; Chameldes, W. L.; Davis, D. D. J. Geophys. Res. 1982, 87, 5015-5017. (23) Chance, B. J. Biol. Chem. 1949, 179, 1311-1330. (24) Cooper, W. J.; Zika, R. G. Science 1983, 220, 711-712. (25) Lowry, J. H.; Smart, R. B.; Maney, K. H. Anal. Chem. 1978, 50, 1303—1309 (26) Rigdon, L. P.; Moody, G. J.; Frazer, J. W. Anal. Chem. 1978, 50,

465-469.

(27) Wong, G. T. F.; Brewer, P. G. J. Mar. Res. 1974, 32, 25-36. (28) Sugam, R. Water Chlorination·, Ann Arbor Science: Ann Arbor, MI, 1983; Vol. 4, pp 653-666.

Received for review February 10,1986. Accepted May 1,1986. This work is from the Ph.D. Dissertation of the senior author.