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Anal. Chem. 1982, 5 4 , 50
5 E \
40
5 30 c
w 20
E
i2
10 0
0
10
20
30
40
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V I A (pg/mL)
Figure 9. A correlation plot comparing the results of identical sets of HSA standard solutions &g/mL) as determined by the microbiuret and V I A methods, respectively. A perfect correlation curve is represented as a broken line.
certainity of measurement in the asymptotic portion (>40 wg/mL) of the VIA calibration curve (Figure 8). Since one may dilute the sample into the lower region, the upper limitation on concentration is not a problem.
ACKNOWLEDGMENT The authors acknowledge the helpful comments of K. R. Wehmeyer, J. P. Zodda, and M. J. Welch. The assistance of J. P. McCarthy with the ICP-AES analysis is gratefully appreciated. LITERATURE CITED Chait, E. M.; Ebersole, R. C. Anal. Chem. 1981, 53, 682A-692A. Nakamura, M.; Dlto, W. R. Lab. Med. 1980, 7 1 , 807-817. Leute, A. K.; Ullman, E. F.; Goldsteln, A.; Herzenberg, L. A. Nature (London), New Bioi. 1972, 236, 93-94. Deaton, C. D.; Maxwell, K. W.; Smith, R. S.;Creveling, R. L. Ciin. Chem. (Winston-Salem, N . C . ) 1976, 22, 1465-1470. O'Donnell, C. M.; Suffin, S.C. Anal. Chem. 1979, 57,33A-40A. Wisdom, G. B. Ciin. Chem. (Winston-Salem, N . C . ) 1976, 22, 1243-1255.
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(7) Scharpe, S. L.; Cooreman, W. M.; Bloome, W. J.; Laekeman, G. M. Ciin. Chem. (Wlnston-Salem, N . C . ) 1976, 22, 733-738. (8) Alexander, P. W.; Maltra, C. Anal. Chem. 1982, 5 4 , 68-71. (9) Meyerhoff, M. E.; Rechnitz, C. A. Anal. Biochem. 1979, 95,483-493. (10) Yuan, Chang-Li; Kaun, S.;Guilbault, G. G. Anal. Chem. 1981, 53, 190-1 93. (11) Weber, S. G.; Purdy, W. C. Anal. Lett. 1979, 12(B1), 1-9. (12) Wehmeyer, K. R.; Halsall, H. 8.; Heineman, W. R. Clin. Chem. (Winston -Salem, N .C .), in press. (13) Flato, J. B. Anal. Chem. 1972, 4 4 , 75A-87A. (14) Copeland, T. R.; Skogerboe, R. K. Anal. Chem. 1974, 4 6 , 1257A1268A. (15) Meares, C. F.; Goodwin, D. A.; Leung, C. S-H.; Giris, A. Y.; Silvester, D. J.; Nunn, A. D.; Lavender, P. J. Proc. Natl. Acad. Sci. 1976, 63, 3803-3806. Krejcarek, G. E.; Tucker, K. L. Biochem. Biophys. Res. Commun. 1977, 7 7 , 581-585. Wagner, S.J.; Welch, M. J. Nut/. Med. 1979, 20, 428-433. Martell, A. E.; Smith, R. M. "Critical Stabllity Constants"; Plenum: New York, 1979; Vol. I, p 281. McCarthy, J. P.; Jackson, M. E.; Ridgway, T. H.; Caruso, J. A. Anal. Chem. 1981, 53, 1512-1514. Kessler, S. W. J . Immunol. 1978, 177, 1482-1490. MacSween, J. M.; Eastwood, S. L. J . Immunol. Methods 1978, 23, 259-267. k h a k i , R. F.; Gill, D. M. Anal. Biochem. 1964, 9 ,401-410. Losev, V. V.; Moledov, A. I. "Encyclopedia of Electrochemistry of the Elements"; Bard, A. J., Ed. ; Marcel Dekker: New York, 1976; Vol V I , P 1. Stankovich, M. T.; Bard, A. J. J . Nectroanai. Chem. 1978, 86, 189-199. Lawson, J. G.; Aivens, D. A. J . Electroanal. Chem. 1967, 75, 193-209. Florence, T. M.; Batley, G. E.; Farrar, Y. J. J . Electroanal. Chem. Interfacial Nectrochem. 1974, 56,301-309. Hardle, G.; van Regenmortel, M. H. V. J . Immunoi. Methods 1977, 15, 305-314. Galzutis, M.; Pesce, A. J.; Lewy. J. E. Microchem. J . 1972, 17, 327-337. Bradford, M. Anal. Biochem. 1978, 7 2 , 248-254.
RECEIVED for review June 23, 1982. Accepted July 29, 1982. This work was supported by NIH Grant AI-16753, and in part by NSF Grant CHE 79-11872 and a summer ACS Analytical Divison Research Fellow sponsored by the ACS Division of Analytical Chemists (M.J.D.).
Bjerrum Plots for the Determination of Systematic Concentration Errors in Titration Data Alex Avdeef," Diane L. Kearney, Jesslca A. Brown, and Alfred R. Chemotti, Jr. Department of Chemistry, Syracuse University, Syracuse, New York
It Is demonstrated how Bjerrum formatlon plots, whlch normally are useful In estlmatlng equilibrium constants, can also be used to determlne systematic concentratlon errors and detect nonldeal electrode responses In pH-metrlc titration data. BJerrumplots for ethylenedlamlne (en), Cu2+-en, citric acld, EDTA (ethylenedlamlnetetraacetlc acld), and ZnzfEDTA systems were used to Illustrate the technique. Examples are presented where a nonlinear regresslon procedure treating total concentratlons as adjustable parameters (along wlth pK,'s) converges to a false mlnlmum. The application of the Bjerrum dlagnosls averts the problem.
In our potentiometric studies of metal-ligand complexation reactions, we frequently titrate ethylenediamine with KOH for the purpose of calibrating our glass electrodes (I, 2). The calibration procedure calls for the nonlinear regression analysis
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of the p H data, where the pK,'s and the concentration of ethylenediamine are treated as adjustable parameters, in a manner similar to that described by Briggs and Steuhr (3). On occasions we have found the refinement calculations to converge to a false minimum. This seems to occur when the initial total concentrations are incorrect by more than 3-5%. For the past 7 years, we have been employing a graphical procedure which practically eliminates the occurrence of false minima in the regression analysis. We describe here the use of Bjerrum plots ( 4 ) as diagnostic aids in the determination of systematic concentration errors in pH-metric titration data. In potentiometric acid-base titrations of ligand (weak acid) or metal-ligand aqueous solutions, Bjerrum formation plots are very useful for the approximate determination of equilibrium constants ( 4 ) . In alkalimetric titrations of solutions containing a ligand, the Bjerrum formation curve refers to the plot of the average number of bound protons, ii,, as a function of pH; with titrations involving both metal and ligand reac-
0003-2700/62/0354-2322$01.25/00 1982 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 54, NO. 13, NOVEMBER 1982
tants, the formation curve refers to the plot of the average number of bound ligands, iiL,vs. pL (pL = -log [L], where [L] is the concentration of the ligand in the fully deprotonated form). Small systematic errors in the concentrations of the reactants can distort the formation curves significantly, to the detriment of the determination of equilibrium constants. Rossotti and Rossotti (4)and Sillen ( 5 ) have pointed out examples of such distortions. We will attempt to present the subject in more detail. From the characteristic distortions of the formation curves it is possible to recognize and correct small errors in the total concentrations of the metal, ligand, and strong acid or base reactants. Nonlinear response of the electrode in the extreme pH regions (pH .C3 or pH >lo) can also be recognized. The procedure for correcting concentration errors is demonstrated by using computer-simulated titration data for solutions of A13+ with 3,5-disulfocatechol (Tiron). Experimental Bjerrum formation curves for the EDTA (ethylenediaminetetraacetic acid), Z P - E D T A , citric acid, ethylenediamine (en), and Cu2+-en systems serve as additional examples of the procedure. We routinely use the Bjerrum formation functions to monitor the progress of potentiometric titrations performed automatically by a milcrocomputer (2). Mistakes in the preparation of the titrated solutions, decomposition of ligands, and electrode or buret malfunctions are immediately apparent from the shapes of the calculated formation curves. EXPERIMENTAL SECTION Reagents. Citric acid monohydrate (Fisher), Na2H2EDTA. 2Hz0 (Aldrich),and KNO:3(J. T. Baker) were used without further purification. “Puratronic” grade Cu(N03),.XH20 and Zm(N03)z.XHz0were obtained from Johnson Matthey Chemicals, Ltd. Stock solutions. All stock solutions were prepared and stored under nitrogen inside of a moisture-saturated, inert atmosphere box (Vacuum Atmospheres). The 1 M HN03titrant solution was prepared from 65% “Ultrapure”nitric acid (Alfa). The 1M KOH titrant solution wa1 prepared from ”Dilut-it”analytical concentrate (J. T. Baker). Both titrants were standardized to 12.0 or pH 12 and consequently that portion of the formation curve was not used to evaluate concentration errors.
ACKNOWLEDGMENT We thank Hans H. Stuting for technical assistance. LITERATURE CITED (1) (2) (3) (4) (5) (6)
(7) (8) (9)
(IO) (11)
(12) (13) (14) (15) (16) (17) (16)
Avdeef. A.; Bucher, J. J. Anal. Chem. 1978, 5 0 , 2137-2142. Brown, J. M.S. Dissertation, Syracuse University, 1981. Briggs, T. N.; Stuehr, J. E. Anal. Chem. 1975, 4 7 , 1916-1920. Rossotti, F. J. C.; Rossotti, H. "The Determination of Stability Constants"; McGraw-Hill: New York. 1961; p 87. Siiien, L. G. Acta Chem. Scand. 1956, 10, 186-202. Rossotti, R. J. C.; Rossotti, H. J . Chem. Educ. 1965, 4 2 , 375. Sweeton, F. H.; Mesmer, R. E.; Baes, C. F., Jr. J . Solution Chem. 1974, 3 , 191. Avdeef, A.; Sofen, S. R.; Bregante, T. L.; Raymond, K. N. J . Am. Chem. SOC.1978, 100, 5362-5370. Avdeef, A,; Raymond, K. N. Inorg. Chem. 1979, 18, 1605-1611. Avdeef, A. Inorg. Chem. 1980, 19, 3081-3086. Avdeef, A. I n "Computational Methods in the Determination of Stability Constants"; Leggett, D. J., Ed.; Plenum: New York; submitted. Haveikova, L.; Barusek, M. Collect. Czech. Chem. Commun. 1969, 3 4 , 3722-3731. Irving, H. M.; Rossotti, H. S. J . Chem. SOC.1954, 2904. Rossotti, F. J. C.; Rossotti, H. "The Determination of Stability Constants"; McGraw-Hili: New York, 1961; p 59. Everett, D. H.; Pinset, B. R. W. R o c . R . SOC.London, Ser. A 1952, 215, 416. Nasanen, R.; Koskinen, M. Acta Chem. Scand. 1964, 18, 1337-1 340. Kodama, M.; Yatsunami, T.; Kimura, E. Inorg. Chem. 1980, 19, 1600- 1602. Anderegg, G . Helv. Chim. Acta 1964, 4 7 , 1801.
RECEIVED for review May 21,1982. Accepted August 9,1982. The research was funded by the donors of the Petroleum Research Fund, administered by the American Chemical Society, and by BRSG Grant SO7 RR07068-14 awarded by the Biomedical Research Support Grant Program, Division of Research Resources, NIH.
