Environ. Sci.
Technol. 1907,21,1135-1136
Duinker,J. C., Eds.; Martinus Nijhoff/Dr. W. Junk: The Hague, 1984; pp 165-179. Kramer, C. I. M. Ph.D. Thesis, University of Groningen, The Netherlands, 1985. PlavliC, M.; Kozar, S.; KrznariC, D.; Bilinski, H.; Branica, M.Mar. Chem. 1980, 9,175. PlavgiC, M.;KrznariC, D.; Branica, M. Mar. Chem. 1982, 11, 17.
Center for Marine Research Zagreb Rudjer BoskoviE: Institute Zagreb, Croatia, Yugoslavia
Ivlca Flu216
SIR: As we read them, Dr. RuiiE‘s comments include two minor issues that require clarification (missing references and use of Scatchard plots) and a major point of disagreement regarding the concept of “total binding capacity” (aka “complexation capacity” or “chelation capacity”). (1) Ignored References. As is clear from the submission date of the articles, 7/9/84, our studies (1,2)had been concluded before publication of the Texel conference proceedings (3) (a copy of which we got for review late in 1984) or the Turner et al. paper (4). In fact, the latter uses the results of a preliminary report on our work. It is not easy to deal with new papers appearing in press during a slow publication process. In that case we did not feel the new articles contained information that modified the thrust of our arguments or our conclusions and decided not to modify our text in the course of review and publication. (2) Ligand Identification from Scatchard Plots. Dr. Ruiie is right, and we were wrong. Two, not three, ligands can be determined from slopes and intercepts of asymptotes of a Scatchard plot. We are particularly contrite to have added this obvious error to an already voluminous literature of misstatements regarding the quantitative interpretation of complexometric titration curves. It is also unfortunate that this error has clearly obfuscated our main point that a Scatchard plot can correspond to many ligands. Two ligands can often be determined with some precision. A third ligand is usually necessary and enough to approximate the data closely in the transition region between the asymptotes. Although ligands in excess of two are poorly defined by the Scatchard method, it is not true that two ligands only can fit any complexometric titration curve. As explained in our paper, this depends on the range of available titration data. (3) Binding Capacity. The “total metal binding capacity” of humic matter is not a particularly useful concept in aquatic chemistry. It is usually taken to represent an elusive total concentration of ligands (LT),the value of which depends on the range of titration data considered and the graphical or numerical technique (and the implied underlying model) used to calculate it. The total binding capacity also provides no information about the ability of humates to solubilize solid-phase or adsorbed metal ions, or about the speciation or free ion activity of a given metal in a sample. Sets of discrete ligands can be used to fit humate complexometric data. To have any kind of meaning and be of any use, however, ligand concentrations must be calculated and reported with their associated stability constants. 0013-936X/87/0921-1135$01.50/0
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Figure 1. Calculated complexometric titrations of a three-ligandsystem (Ll1 = 20 nM, log K 1 = 9.5; L,, = 100 nM, log K 2 = 7.5; L,, = 500 nM, log K, = 5.5) over two different concentration ranges. In panel A, quasi-linear behavior is observed with very low intercept (ca.50 nM)
and a slope much less than unity (Le., the slope of an appropriate Calibration line). In panel B, quasi-linear behavior is observed with a slope approaching unity. However, the intercept (ca. 115 nm) is much less than that of the actual asymptote (dashed line),which yields the “total binding capacity” of 620 nM.
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Figure 2. Calculated complexometrictitrations identical with those of Figure 1, using the format recommended by RuiiE. Again, quasi-linear
behavior is observed much before the actual asymptote is approached. The corresponding apparent slope-the Inverse of which yields the “binding capacity”4ependsstrongly on the range of data considered. Even at values of free (or inorganic) metal on the order of the total ligand (B), the slope Is still markedly too high and the titration curve much below its asymptote (dashed line). The total concentration of a well-defined ligand can be determined by several graphical methods including Scatchard’s. For example, LT can be obtained by the following: (1)ascertaining the inflection point in a log [MI vs. log MT graph-a horrible technique we certainly did not advocate, Dr. Ruiie’s comments notwithstanding (2) extrapolating to the abscissa a plot of [MI vs. MT as is usually done with polarographic or amperometric data (3) measuring the slope of the asymptote in a plot of [M]/(MT - [MI) vs. [MI as advertised by RuiiE in his comments and his earlier publications However, as can be seen in Figures 1and 2, in a complex system both of the two latter methods may lead to answers that depend chiefly on the range of data considered. In the figures where three ligands axe considered, approximate linear behavior is obtained much before the actual asymptotes are approached. This is particularly misleading in the case of the RuiiE graph, which is not constrained by the slope of a calibration line. The situation is no doubt worse in the case of humic materials, which are probably not a simple mixture of three ligands and may contain large concentrations of very weak complexing sites. The difficulty in the experimental and mathematical definition of L T is however only the least of the many evils associated with the notion of “binding capacity”. As an extensive parameter it promotes the notion that a certain number of moles of a metal can be bound or made nonreactive or nontoxic. By contrast, the central scientific issue of metal complexation in natural waters relates in
0 1987 American Chemical Society
Environ. Sci. Technol., Vol. 21, No. 11, 1987 1135
fact to an intensive parameter, the free metal ion activity. Complexation of a metal by natural ligands controls the free metal ion activity, which in turn determines the thermodynamic (and sometimes kinetic) reactivity of the metal with other chemical and biological entities.
Literature Cited (1) Dzombak, D. A.; Fish, W.; Morel, F. M. M. Environ. Sci. Technol. 1986, 20, 669-675. (2) Fish, W.; Dzombak, D. A,; Morel, F. M. M. Enuiron. Sci. Technol. 1986, 20, 676-683. (3) Proceedings of the International Symposium on Complexation of Trace Metals in Natural Waters, The Neth-
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erlands Institute for Sea Research at Texel, May 24,1983; Kramer, C. I. M., Duinker, J. C., Eds.; Martinus Nijhoff/Dr. W. J u n k The Hague, 1984; 448 pp. (4) Turner, D. R.; Varney, M. S.; Whitfield, M.; Mantoura, R. F. C.; Riley, J. P. Geochim. Cosmochim. Acta 1986, 50, 289-297.
F. M. M. Morel," D. A. Dzombak, W. Fisht Ralph M. Parsons Laboratory, 48-425 Massachusetts Institute of Technology Cambridge, Massachusetts 02139
'With the help of J. Hering.
