Environ. Sci. Technol. 1996, 30, 3640-3641
Response to Comment on “Determination of Metal (Bi)Sulfide Stability Constants of Mn2+, Fe2+, Co2+, Ni2+, Cu2+, and Zn2+ by Voltammetric Methods” SIR: In the following, we systematically address Davison’s (1) comment concerning our paper (2) presenting voltammetric determinations of metal (bi)sulfide stability constants of Mn2+, Fe2+, Co2+, and Ni2+. In addition, we provide previously unpublished data independently confirming our results. (a) Davison (1) notes some concerns with our application (2) of the DeFord and Hume (3) approach as modified by Heath and Hefter (4) to the determination of stability constants for bisulfide with the +2 cations of Mn, Fe, Co, and Ni. A principle reason for this is that the cumulative constants found for the species MSH+, M2(SH)3+, and M3(SH)5+ are similar. This agreement is surprising to Davison (1) based on comparing constants for organic ligands with sulfur binding atoms with multiple binding sites. For a system in which several stepwise complexes are formed, the expression of DeFord and Hume (3) is given as eq 1 where m is the the uncomplexed species, c is the complexed species, and X is the material complexing the electroactive species. In our case, added metal (Mn, Fe, Co, Ni) complexes the bisulfide, the electroactive species:
(Ep)m - (Ep)c )
Dc1/2 ln nF D 1/2 m
RT
N
fm fxjβjCxj
j)0
fMX
∑
(1)
The stability constants can be determined from
F0(X) )
∑β {X}
n
n
) β0 + β1[X] + β2[X]2 + ... + βn[X]n (2)
where F0(x) is the sum of all complexes, βn is the overall stability constant of the nth complex, [X] is the analytical concentration of the ligand (metal ion in our case), and β0 ) 1 for the zeroth complex. F0(X) is related to the current and potential data by
F0(X) ) antilog {[0.434 nF/RT][∆Ep] + [log (Ip)m/(Ip)c]} (3) where ∆Ep ) (Ep)m - (Ep)c, and Ip indicates peak current. Clearly from eqs 1-3, ∆Ep is NOT directly dependent on the concentration of sulfide, the electroactive species, as stated by Davison (1). As stated in the Experimental Section (2), we used 1-10 µM sulfide for our work with no change in the stability constants determined. Davison (1) actually states that we need to use 10 µM so we do not see the reason for his comments. In our Figure 1 (ref 2), we actually showed a case where the concentration of the electroactive species is 2 µM and not 1 µM as incorrectly stated by Davison (1). (b) In his Figure 1, Davison (1) makes “by-eye” estimates from our data by drawing limiting slopes to our curves. This is an approximation at best and is not consistent with
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ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 30, NO. 12, 1996
TABLE 1
Representative Data for Titration of Bisulfide with Ni(II) in Full-Strength Seawater Using a 1-mV Scan Increment [Ni] (µM)
Ep (V)
F0
F1(105)
0.000 2.490 3.480 4.470 5.450 6.440 7.420 8.400 9.380 10.40
-0.6200 -0.6167 -0.6144 -0.6110 -0.6065 -0.6025 -0.5997 -0.5978 -0.5930 -0.5892
1.296 1.546 2.014 2.858 3.901 4.863 5.645 8.169 10.98
1.19 1.57 2.27 3.41 4.51 5.20 5.53 7.64 9.63
a These data are plotted in Figure 1. ∆E and F are larger than that p 0 in Figure 1 (ref 2).
the recommendation to perform least squares fits, which remove experimenter bias from data analysis (5). For example, Davison’s Figure 1c is inappropriate because it shows a horizontal slope parallel to the x-axis, which is dependent on the approximations made in his Figure 1b that ignore the upper points of the curve. Calculations ignoring the upper points usually increase not decrease the β values. In addition, β1 should be calculated using F1 rather than estimated from F0. The need for greater Ep shifts than 2 mV as noted by Davison (1) has been observed by us in other experiments (we have well over 50 in the 1-10 µM sulfide range). (c) The 2 mV scan increment is typical for our work. However, we performed triplicate runs on each titration point, and the precision of these replicate runs is always better than 1 mV, and frequently there is no change in Ep for replicates which is why we estimate a tenth of a mV. This is consistent with previous practice, including Heath and Hefter (4). Furthermore, we have performed the work with a more sensitive analyzer, which has 1 mV scan increment capability. A data set for 2 µM HS- is shown in Table 1 and Figure 1. These clearly confirm our β values and demonstrate that Davison’s criticisms are at best misplaced. (d) Another reason for replicates on each titration point is to ensure that the Ep does not vary in solutions where the IAP can exceed the Ksp. As Bond and Hefter (6) indicate, the use of rapid ac polarographic techniques [which are similar to the square wave voltammetric (SWV) method we use] is possible to determine β values on sparingly soluble systems provided that there is no change in Ep over time after addition of the cation and anion. No Ep shift indicates that complex equilibria is more rapidly established than solubility equilibria. Thus, successful β determination is governed by precipitation kinetics, which are not related to the solubility product. (e) Davison (1) indicated that sulfide forms a HgS film at potentials more positive than -0.6 V, and this may compromise peak reversibility. To verify reversibility for the sulfide peak at low concentrations, Luther and Ferdelman (7) obtained reliable pKa data for pK1 of H2S using the reversible expressions derived by Meites (8). In sulfide titrations with metal ions, we obtained similar β results
S0013-936X(96)02005-6 CCC: $12.00
1996 American Chemical Society
have confidence in our titration results since only one metal is present in significant concentration. (g) From a chemical perspective, inspection of the β values for successive metal complexes with halide ions and hydroxide (14) frequently show similar behavior as we observe for HS- with added metal; i.e., the successive constants are typically similar. The data summarized in Table 2 (ref 2) show that the log β for OH- and Cl- complexes with Mn2+, Fe2+, Co2+, and Ni2+ are not very different as we observe for the HS- complexes. Our results are also consistent with HS- being a stronger binder than OH- and Cl- for soft +2 metals. Thus, it is not appropriate for Davison (1) to compare multidentate ligands to monodentate ligands. FIGURE 1. F1(X) versus concentration plot for another titration of sulfide with Ni(II) in full-strength seawater using a 1-mV scan increment. The intercept and coefficients of the quadratic fit of the F1 plot yields log β1 (4.83), log β 2 (9.40), and log β3 (15.9); the β values agree with those reported (2). The intercept of the exponential fit to F1 yields log β1 (4.85), which is within 0.02 log unit of the intercept of the quadratic fit. “By-eye” fits cannot explain the variance in the data whereas curve fitting techniques quantitatively explain 97% or better of the variance.
when scans were begun at -0.1 or -0.4 V and when the scan was from -1.5 to -0.1 V. The reason the method works in either direction is that the wave is reversible as indicated by the forward and reverse scans of the square wave in accordance with the work of Turner et al (9). Also, we observe no other peaks due to adsorption phenomena in our SWV voltammograms; adsorption phenomena are likely to occur in the DPP method that Davison discusses in his comment (1). Furthermore, we are working at sulfide levels where a monolayer or less of film usually forms; as noted by Davision (10), this leads to a good analytical signal in the DPP and NPP methods and as we observe in SWV. With fast scan methods and low concentrations, film formation is not a problem (11). Performing calculations with and without the current function in the calculation of F0(X) (eq 3) indicates that the β values are similar and that the ‘stripping’ current resulting from a positive initial potential (without deposition and stirring) does not affect our results. Lastly, stripping measurements after deposition and solution stirring have been used to determine β’s by determining shifts in Ep (12); in very low concentration cases, pseudopolarograms (discrete measurements of stripping current as deposition potential is varied) can be recorded rather than scans over the complete potential range as we used. For all our measurements, there was no deposition with solution stirring; solutions were quiescent so that sulfide transport to the electrode was diffusion controlled. (f) It is correct that we have noted broadening of the sulfide peak in deposition experiments with stirring on natural seawater samples (13) at nM levels when more than one metal is present at similar concentrations. Of the metals tested in our study, only Cu(II) added to sulfide gives broadened peaks after deposition while stirring the solution; we do not observe a sulfide signal when the Cu concentration g the sulfide concentration in experiments where we have a positive initial potential and do not stir. Thus, we
(h) Lastly, we caution against indiscriminate use of β values. As noted in Luther and Ferdelman (7) as well as in ref 2, acid-base titrations of sulfide with Mn2+, Fe2+, Co2+, and Ni2+ indicate that HS- complexes clearly exist from pH 8 to pH 10; thus, our β values are valid for that range. When the pH e 7, these are protonated to form H2S complexes that dissociate. Between pH 7 and pH 8, there may be an undefined transition point for conversion between HS- and H2S complexes. Thus metal-sulfide complexes change speciation with pH as expected. We have not made an effort to determine the stoichiometry and β values of H2S complexes for Mn2+, Fe2+, Co2+, and Ni2+ because dissociation occurs.
Literature Cited (1) Davison, W. Environ. Sci. Technol. 1996, 30, 3638-3639. (2) Luther, G. W., III; Rickard, D.; Theberge, S. M.; Olroyd, A. Environ. Sci. Technol. 1996, 30, 671-679. (3) DeFord, D. D.; Hume, D. N. J. Am. Chem. Soc. 1951, 73, 53215322. (4) Heath, G. A.; Hefter, G. J. Electroanal. Chem. 1977, 84, 295302. (5) Bond, A. M. Coord. Chem. Rev. 1971, 6, 377-405. (6) Bond, A. M.; Hefter, G. Electroanal. Chem. Interfac. Electrochem. 1972, 34, 227-237. (7) Luther, G. W., III; Ferdelman, T. G. Environ. Sci. Technol. 1993, 27, 1154-1163. (8) Meites, L. Polarographic Techniques, 2nd ed.; Wiley Interscience: New York, 1965. (9) Turner, J. A.; Abel, R. H.; Osteryoung, R. A. Anal. Chem. 1975, 47, 1343-1347. (10) Davison, W. Anal. Proceedings 1991, 28, 59-61. (11) Canterford, D. R.; Buchanan, A. S.; Bond, A. M. 1973. Anal. Chem. 1973, 45, 1327-1331. (12) Brown, S. D.; Kowalski, B. R. Anal. Chem. 1979, 51, 2133-2139. (13) Luther, G. W., III; Tsamakis, E. Mar. Chem. 1989, 27, 165-177. (14) Smith, R. M.; Martell, A. E. Critical Stability Constants; Plenum Press: New York, 1989; Vols. 1-6.
George W. Luther, III* and Stephen M. Theberge College of Marine Studies University of Delaware Lewes, Delaware 19958
David T. Rickard and Anthony Oldroyd Department of Earth Sciences University of Wales Cardiff CF1 3YE, Wales, U.K. ES962005V
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