Envlron. Sci. Technol. 1093, 27,520-529
Modeling the Competition between Alkaline Earth Cations and Trace Metal Species for Binding by Humic Substances Edward Tipping
Institute of Freshwater Ecology, Ambleside, Cumbria, LA22 OLP, United Kingdom
Humic ion-binding model V is used to interpret competition effects in the binding of trace metal species and alkaline earth cations (Mg2+,Ca2+)by fulvic-type humic substances. Intrinsic equilibrium constants for the alkaline earths are derived from literature data, and the values estimated from direct binding data are shown to be compatible with the results of competition studies involving copper. Within the model, three mechanisms of competition are possible, these being direct competition at discrete sites, competition for counterion accumulation, and reduction in net electrical charge on the humic molecule by alkaline earth cation binding to certain sites, which diminishes the electrostatic contribution to trace metal binding at other sites. The first mechanism is most significant for divalent trace metals having relatively high affinities for humic Substances. Features of model V that permit compatibility between competition data and direct binding data are (a) sites with different relative affinities for different metals, (b) the presence of both monodentate and bidentate sites, and (c) the contribution of nonspecific counterion accumulation to alkaline earth binding.
Introduction Binding by humic substances in waters and soils is recognized as potentially important in controlling the chemical speciation and transport of trace metals in environmental aquatic systems (1-4). With the aim of predicting the extents of trace metal-humic interaction, an equilibrium discrete site-electrostatic model (model V) has recently been developed and parameters for a number of metal species have been estimated (5). Model V allows metal binding to be predicted at different pH and ionic strength values and includes the possibility of competition among different metal species. In general, the most important competition effects in natural systems are likely to be due to the alkaline earth cations (Mg2+,Ca2+),the high concentrations of which will compensate for their relatively weak humic-binding affinities. The literature contains several reports of experimental studies in which the competition between Mg2+or Ca2+ and copper species for binding by humic substances has been studied (6-9).These data are analyzed in the present paper using model V, in order to assess the extent to which the observed competition effects are compatible with model parameters (metal-proton exchange equilibrium Constants) estimated from results of experiments in which binding of the competing metal species was studied separately. The present work deals with fulvic-type material-either fulvic acids per se or aquatic humic matter-but the approach should be applicable to humic substances in general. Model Description Model V has been described in detail previously (5). Essentially, the humic substances are represented by a hypothetical homogeneous compound with molecular dimensions similar to the weight-average values of the real material. The algebra of the model is given in the Appendix. The main features are as follows. 520
Environ. Sci. Technol., Vol. 27, No. 3, 1993
(a) Discrete Proton-Binding Sites (Type A and Type B). Within each type, there are four different sites present in equal abundances. The type A sites are numbered 1-4, the type B sites, 5-8. The intrinsic (Le,, charge-independent) pK values (for proton dissociation) are described by the parameters pKA and pKB (central values) and ApKAand ApKB (spreads of values). There are n type A sites (approximately coinciding with humic COOH content) and n / 2 type B sites (phenolic OH and other weak acid moieties). Thus, five parameters are used to characterize the proton-binding sites. The formulation of sites in this way is admittedly somewhat arbitrary, and other arrangements would undoubtedly permit equally good data fits, although it is unlikely that less than five parameters would be adequate in any model. The approach taken was influenced by the desire to describe the binding of metal species economically and to include the possibility of both monodentate and bidentate metal binding. (b) Metal Binding at Single Proton Sites (Monodentate) or by Bidentate Complexation at Specified Pairs of Sites. These interactions are described by intrinsic equilibrium constants for metal-proton exchange. For each metal species there are two such equilibrium constants, one for each set of proton-binding sites, denoted by PKMHA and PKMHB. The extent to which bidentate binding is possible is constrained by the proximity factor (5),which defines, on the basis of molecular geometry and by assuming a random positioning of proton-binding sites on the molecular surface, the likelihood of pairs of proton-binding sites being close enough to form bidentate sites. For fulvic-type material, a proximity factor of 0.4 has been estimated (5), which means that 40% of the proton-binding sites are sufficiently close to form bidentate sites. Of the 36 possible pairings of the 8 proton-binding sites, 12 equally abundant representative pairings are chosen as the bidentate sites (cf. ref 5 and Tables VI and VII). Equilibrium constants for metal-proton exchange at the bidentate sites are obtained simply by multiplying the constants for the individual proton-binding sites; on the basis of equilibrium constants for simple diprotic acids, a possible “chelate effect” is ignored (5). The monodentate sites correspond to proton-binding sites that are not involved in making up the bidentate sites and are denoted by MON(i), where i is the proton-binding site in question. The bidentate sites are denoted by BID(ij), where i and j are the constituent proton-binding sites. (c) Electrostatic Influence on Binding at Discrete Sites. The net charge on the humic material affects proton and metal binding at discrete sites by modifying intrinsic equilibrium constants to account for enhanced (or diminished) interaction as a result of electrostatic attraction (or repulsion) at the discrete binding sites. The modifying terms are of the form exp(-2wzZ) where z and 2 are the charges on the proton or metal species and the humic matter, respectively, and w is the electrostatic interaction factor, empirically defined in the case of fulvic-type materials by the expression w = P log I (1)
0013-936X/93/0927-0520$04.00/0
0 1993 American Chemical Society
Table I. Fixed Model V Parameters for Fulvic-Type MaterialsR parameter
value
parameter
value
10% (mol g-’) PK A pKB
4.7 3.3 9.6 3.3 5.5
P radius (nm) mol w t
-103 0.8 1500 0.4
b K A
APKB
fPR
Values for the first six were obtained by fitting data for proton binding: values for the molecular radius and proximity factor were estimated from data on humic molecular weight and density and from geometrical considerations. See ref 5 for details.
up,)
(I
where P is a constant and I is ionic strength. (d) Nonspecific Binding. This arises from the same mechanism as (c), i.e., the attraction of counterions, or the repulsion of co-ions, by the charge on the humic molecule. Whereas in (c) the effect on binding a t specific sites is considered, via an enhanced activity close to the molecular surface, the concern here is the calculation of the extent of counterion accumulation per se around the molecule. In model V the accumulation is governed entirely by counterion charge, with ions of higher charge being favored over those of lower charge according to simplified Donnan expressions. To calculate counterion accumulation it is necessary to specify the approximate molecular weight and radius of the humic molecule and the thickness of the diffuse part of the electrical double layer. Fulvic-type materials, as considered in the present work, are assumed to have a molecular weight of 1500 and a radius of 0.8 nm (5). Diffuse layer thickness is taken to be equal to the Debye-Hiickel characteristic length (l/& From these factors, the volume of diffuse layer water can be calculated. Within this volume there is sufficient countercharge exactly to balance the net humic charge. Binding of a given species by this nonspecific mechanism depends strongly upon the concentrations and charges of the other counterions present. Counterion accumulation permits any species to bind to humic material, as long as it carries an opposite charge, whereas specific binding is restricted to the parent species and ita hydrolysis product(s) (see below). Model V is one of several current models being developed to describe metal and proton binding by humic substances. In that the model considers the influence of electrostatic effects on binding at specific sites, it is similar to the models of Marinsky and co-workers (10, II), De Wit et al. (12),and Bartschat et al. (13). The model V electrostatic submodel is the simplest and most empirical; the most sophisticated is that of Bartschat et al. (13),which not only employs an “oligoelectrolyte”description but also
considers the variation of the electrostatic effect with molecular size within a given humic sample. Other models do not consider electrostatic effects explicitly, although recourse has been made to the estimation of humic activity coefficients, on the basis of approximate net humic charge (7,14). Perhaps the greatest divergence among models is in the description of binding sites. Whereas model V and some other models (7, 10, 11, 13) postulate a relatively small number of discrete sites, others (12,14-16) view the sites in terms of a continuum frequency distribution of binding energies (equilibrium constants).
Data Fitting In the present study, when metal-binding data obtained by direct measurement are considered, it is assumed that the parameters for proton binding are fixed at the average values previously determined (5) from a number of published data sets. The fiied parameters are given in Table I. From the average pK and ApK values, the pK values of the eight proton-dissociating groups are calculated to and 12.40. In one be 1.59,2.70,3.82,4.93,6.88,8.72,10.56, case considered in the present work ( I n , metal binding is inferred from the displacement of a proton titration w e , and this requires the particular set of proton-binding parameters for the humic material in question to be used. Variations of binding with temperature are assumed to be negligible; most of the data refer to the temperature range 20-25 “C. Fitting of parameters was carried out using the Nelder-Mead polytope method published by Nash and Walker-Smith (18). Parameter standard errors were estimated by the jackknife technique (19), which involves the stepwise omission of data points from a given data set, together with optimization of parameters at each step, in order to generate sets of upseudoparametersn. The variability in the pseudoparameters is then used to estimate parameter dispersion. In the present work, this approach was found satisfactory for all the cases examined except one (data set CACuMg; see Table V), where the sensitivity of the parameters to data point omission was too great to allow sensible pseudovalues to be obtained. Binding of Mg2+ and Ca2+ by Fulvic-Type Material Several values of PKMHA and pKMHBfor these species have been reported previously (5) and are summarized in Table 11. It is noteworthy that the standard errors for the pKvalues are invariably smaller than those for pKThis is because, within the model, the type A sites contribute most to metal binding, especially at the acid-toneutral pH values to which most of the experimental data refer. In the present work, three additional pairs of pKMH
Table 11. Parameters for Mg2+and Ca2+Binding by Fulvic-Type Materials” data set
no. of data
SCSMg DA2Ca DA3Ca HACa MSCa MASCa MAS2Ca SCSCa TACa mean for Ca2+
2 30 60 18 19 74 87 2 13
PH 3.5-5.0 5.0-9.0 5.0-9.0 8.2 4.0-7.7 3.8-8.5 3.5-8.0 3.5-5.0 3.5-6.1
P[Ml 5.0 2.0-3.2 2.0-3.1 3.4-6.9 3.8-4.1 3.4-4.7 3.4-4.6 5.3 2.5
rmse PKMHA PKMHB 1 (2.37) (26.0) 1 2.97 (0.07) 6.63 (0.08) 0.06 1 3.18 (0.03) 7.97 (0.23) 0.05 1.1 1.93 (0.03) 8.73 (4.09) 0.13 1-2 1.86 (0.06) 6.03 (0.41) 0.08 1-2 1.73 (0.02) 7.02 (0.24) 0.13 1-2 1.79 (0.02) 7.24 (0.24) 0.13 1 (2.01) (26.0) 2 2.82 (0.08) 6.26 (0.40) 0.06 2.3 7.1 Data set codes are as in ref 5 and refer to author name, source of humic material (A, aquatic; S, soil), and metal under investigation. The original data are in references as follows: DA2Ca and DA3Ca (20), HACa (a,MSCa (21),MatSCa and MatS2Ca (23), SCSMg and SCSCa (22),and TACa (17). The rmse value refers to residuals in pv, except for the TACa data set, where it refers to residuals in pH. Values from the data of Schnitzer and Skinner (22) are based on essentially only two data points in each case, and so values of rmse are not meaningful. The mean values for Ca2+were calculated by omitting the SCSCa results. PV 5.1-5.3 2.7-3.6 2.9-3.7 3.1-5.1 2.9-3.6 2.9-3.9 3.0-4.6 4.9-5.6 2.7-3.2
PI
Environ. Sci. Technol., Vol. 27, No. 3, 1993 521
Table 111. Parameters Estimated from the Results of Competition Experiments"
-
3.0
BACuCa I = 0.01M
--
4.0 --
=i
a 3'0
I
11..
1..
I = 0.1M
L 4
5
6
7
8
PH Figure 1. Binding of Ca2" by burentide sol1 fulvic acld. The pv of the ordinate refers to -log (mole of Ca2+ bound per gram of fuivic acld). The points are the experimental data of Mathuthu (23)and refer to total calcium concentrations of (0, w), 2 X i t 4 (0,A),and 4 X lo-' M (0). The continuous llnes are model V fRs, obtained by adjusting PKMHA and PKMH, (see text).
values are obtained, by analysis of the data sets of Mathuthu (23) and Tipping et al. (17). The results of Mathuthu (23)were obtained for two soil fulvic acid samples by determining free concentrations of Ca2+with an ionspecific electrode. The results refer to several ionic strengths and metal/fulvic acid ratios, in the pH range 3-9. Values of v (mole of metal bound per gram of humic matter) were calculated from the raw data, and optimization was performed by minimizing the sum of the squared residuals in pv (p = -logl,,). The results are summarized in Table 11. Observed and fitted values of pv for one of the data sets are plotted in Figure 1. It is found that the model reproduces both pH and ionic strength trends, and it should be noted that the adjustments of PKMHA and PKMHB actually have little effect upon these, both of them being largely governed by the fixed parameters obtained from proton-binding data (Table I). As found for the other alkaline earth data sets (Table 11), the data enabled good definition of PKMHA,but PKMHBis relatively poorly defined, as shown by the large standard error for this parameter. The results of Tipping et al. (17) refer to streamwater humic substances (assumed to be predominantly fulvic-type material) and are in the form of a titration curve, which differs from that obtained in the absence of calcium because of proton displacement by bound metal. The observation of a displaced titration curve is itself evidence that specific binding (i.e., at discrete sites) occurs, since if the Ca2+were bound purely nonspecifically (as a counterion) only a small amount of proton displacement (from the diffuse layer) would be expected. Parameter estimation was performed by minimizing the sum of the squared residuals in pH. Again pKis much better defined than PKMHB (Table 11). From the full collection of available PKMM and PKMHB values for Mg2+and Ca2+,it is seen that the parameter 522
23 5.0-6.5
CACuMg 24 4.4-9.0
1
1
3.7-4.1 5.1-5.5 2.4-3.7 1.63 (0.01) 4.38 (0.03) 2.95 (0.05) 7.82 (1.86) 0.01
4.0-4.5 6.2-10.1 2-3* 1.00 (0.09) 3.48 (0.20) 2.76 (0.14) 7.37 (0.23) 0.14
MACuCa 44 6 1.5-3.0 2.8-4.7 4.7-9.2 2-3* 1.00 (0.09) 3.20 (0.22) 2.21 (0.21) 9.77 (4.56) 0.14
"An asterisk in the summary data indicates that they include results in the absence of the alkaline earth cation. Ionic strength (mol L-l) is abbreviated by I, and AE stands for alkaline earth. The CACuMg data set was obtained from plota presented in ref 7, by taking approximately every third data point. For the BACuCa and MACuCa data seta, the rmse value refers to residuals in pu; for the CACuMg set, it refers to p[Cu2+].
4.0
5.0
no. of points PH PI PVC" P[CUl ~[Cal PKMHA(CU) PK,H,(CU) PKMHA(AE) PKMHB(AE) rmse
Envlron. Sci. Technoi., Voi. 27, No. 3, 1993
values cover moderately wide ranges, 1.7-3.2 for PKMHA and 6.0-8.7 for PKMHB Leaving aside experimental error as a reason for the observed ranges, this suggests appreciable variability among fulvic-type materials with respect to the factors in model V that determine metal binding. These factors include not only the strength of the fulvicmetal interactions per se (as quantified by pKMHAand PKMHB)but also the binding site densities, the relative positioning of sites on the humic molecule (proximity factor), the proton-binding characteristics, and the electrostatic terms. For most literature data, there is insufficient background information to describe the protonbinding characteristics of an individual humic isolate adequately, and so application of the model requires the use of average values from other available studies. As a result, any deviations from the assumed proton-binding behavior will affect the values of pKand pKm, which will take on values different from the ideal case in order to accommodate deviations from average behavior in the other factors. Therefore, the observed variations in pKm values do not simply reflect variability in humic affinity for the alkaline earths. Competition Studies The literature contains four studies in which the influence of Mg2+or Ca2+on copper binding by aquatic humic matter has been examined. The published data provide a means of testing predictions of competition effecta, based upon the separately determined parameter values for copper and the alkaline earth cations. Buffle et al. (6) worked with an organic-richmarsh water that had been concentrated by a freezing process. They measured copper binding with an ion-specific electrode as a function of added Ca2+over the pH range of 5-6.5. In order to apply model V, the reported transformed data were converted to values of vcu and free Cu2+concentration. Values of pKand pKfor both Cu2+and Ca2+ were estimated by minimizing the residuals in pvcu (Table 111, Figure 2). The best-fit values of PKMHA and PKMHB for Cu2+are somewhat greater (by 0.5-1.0 log unit) than has been found from the results of experiments with humic matter isolated more conventionally (5),while the values for Ca2+are within the ranges of values tabulated in Table 11. Cabaniss and Shuman (7) also used an ion-specific electrode to examine competition by Mg2+and by Ca2+. Results were presented from an experiment in which the
5.0 I
5
0 0
1
3
2
10
5
4
Flgure 2. Effect of Ca2+ on the binding of copper by organic matter in freezeconcentrated marsh water, as determined by Buffle et ai. (6). The points are experimental resuits; the continuous lines are model V fits, obtained by adjusting pKMHA and pK, values for calcium and copper.
10
I
c
91-
71
4
5
6
7
8
I
I
I
9
8
7
6
5
4
PPJI
1 o3 [ca], mol I-'
I
1
9
PH Flgure 3. Effect of Mg2+on copper binding by Suwannee River fulvlc acid, as determined by Cabaniss and Shuman (7). The points are concentrations of zero (e),lo3 experimentai resuits, referring to (0),and M (m). The continuous lines are model V fits, obtained by adjusting pK ,,, and pK ,,, values for magnesium and copper.
w2+
free concentration of Cu2+was followed over a pH range of 4.4-9.0,for various concentrations of Mg2+,at a fixed concentration of aquatic fulvic acid. The conditions were such that the value of v was nearly constant, because nearly all the copper was bound. Therefore, in applying model V, optimization was done by minimizing residuals in ~ [ C U ] . As in previous work (5), it was assumed initially that the fulvic acid was able to bind the hydrolysis products of Cu2+ [CuOH+,Cu(OH),], and the intrinsic equilibrium constants for the binding of these species were assumed equal to that for Cu2+itself (but see below). The results of the optimization are given in Table 111, and the experimental results and model fits are plotted in Figure 3. The values of p K m and pKfor Cu2+(1.01and 3.47,respectively) are close to those of 1.09 and 3.03 estimated previously (5) from data obtained by the same authors in a separate experiment, in which the fulvic acid was titrated with copper at several (constant) pH values. The pKm values for Mg2+appear reasonably compatible with those listed
Figure 4. Copper binding by Suwannee River fuivlc acid at pH 6, determined by McKnlght and Wershaw (9). The points are eXperC M NaN03 mental resuits for different background electrolytes: M NaN03(0),lo3 M Ce(NO& (O),and M Ce(N03), (O), The continuous lines are model V fits, obtained by adlusting pK, and PKMH, values for calcium and copper.
m.
in Table 11, bearing in mind the observation of Cabaniss and Shuman that similar competition effects are exhibited by both Mg2+and Ca2+. McKnight and Wershaw (9)measured Cu2+binding by the same streamwater fulvic acid that was studied by Cabaniss and Shuman (7), also using an ion-specific electrode, in the absence and presence of calcium. Their results are plotted in Figure 4,together with best-fit model plots, obtained by minimization of the residuals in pv, with optimization of the PKMH values for both Cu2+and Ca2+. Model V predicts (a) a greater influence of ionic strength on copper binding and (b) a more progressive effect of Ca2+ than were observed in the experiments of McKnight and Wershaw. However, the model does reproduce the major trends in the data reasonably well (Figure 4). Again, the best-fit pKmA and PKMHB values for Ca2+are within the ranges given in Table 11. Hering and Morel (8) worked with an aquatic humic acid, which is assumed here to have properties sufficiently similar to those of fulvic acid for the same fiied model V parameters (Table I) to apply. The Hering-Morel study is of special interest, because it involved the separate direct measurements of Cu and Ca binding by the same humic sample, and also the examination of competition effects (which were found to be slight). Thus the separately estimated PKMH values can be combined within model V in order to predict the competition results. The pKMm and PKMHB values for calcium binding were estimated in a previous study (5) and are presented in Table 11. The results for Cu2+ refer to a considerably higher ionic strength (0.5 M), and in order to analyze the data, it was assumed that the extended Debye-Htickel equation could be applied. Values of PKMMand pKMm for CuOH+ and CU(OH)~ were assumed to be the same as those for Cu2+, as in the analysis of the Cabaniss-Shuman data (7) described above. In common with Hering and Morel (8),it was assumed that carbonate complexes of Cu, which accounted for much of the inorganic copper, do not bind specifically to the humic material. The nonspecific binding of these species by counterion accumulation can be discounted because of the high ionic strength. Optimization gave p K ~ m and pKfor the copper species of 1.26 (SE Environ. Sci. Technoi., Voi. 27, No. 3, 1993 b23
c Table IV. Reanalysis of the Data Sets Calcium Binding I 3.5 c
of Table I1 for
refits (PKMHB fixed) rmse rmse data set pKMHA PKMHB in pv PKMHA in Pu DA2Ca 2.97 (0.07) 6.63 (0.08) 0.06 2.69 (0.10) 0.09 DA3Ca 3.18 (0.03) 7.97 (0.23) 0.05 3.08 (0.07) 0.05 HACa 1.93 (0.03) 8.73 (4.09) 0.13 1.93 (0.03) 0.13 MSCa 1.86 (0.06) 6.03 (0.41) 0.08 1.78 (0.05) 0.09 MASCa 1.73 (0.02) 7.02 (0.24) 0.14 1.72 (0.04) 0.14 MAS2Ca 1.79 (0.02) 7.24 (0.24) 0.13 1.79 (0.02) 0.13 TACa 2.82 (0.08) 6.26 (0.40) 0.06 2.55 (0.20) 0.13 original fits
I '
/
Estimates were made of D K ~with ~ DK, ~ .MuR fixed a t 8.5.
!
*:
i
L
1
10.0
9.5
1
9.0
8.5
PCCUI Flgure 5. Copper blndlng by Suwannee River humic acid at pH 8.25 and I = 0.5 M, determlned by Herlng and Morel (8). The points are experimental data, obtained at concentrations of humic substances of 3 X lo-' (0)and 6 X (0)g L-', and In the absence of calcium. The continuous line Is the model V flt, with pK,,, = 1.26 and pK, = 2.52. The broken lines were calculated with model V for compemion M Ca2+,wlth the following palrs of values of pK, and pKM: by 1.93 and 8.73 (- -) and 1.93 and 7.1 (-). Herlng and Morel found that M Ca had llttle effect on copper binding. the presence of
-
= 0.05) and 2.52 (SE = 0.06),respectively, values which are reasonably similar to those obtained from other workers' data (5). The observed data and fitted curve of Figure 5 show that model V accounts only approximately for the experimental observations, the measured binding being somewhat less sensitive to p[Cu] than is calculated. (It should be borne in mind, however, that the primary aim of model V is to explain ion binding by humic materials within a single conceptual framework and to establish coherent relationships among results for different metals under different conditions. By its generalizing nature, the model cannot be expected always to produce precise fits to individual data sets, especially over relatively narrow ranges of free and bound metal concentrations.) When the separately determined values of PKMHA and PKMHB for copper and calcium are used to calculate the effect of Ca2+on copper binding, only a small competition effect is predicted (Figure 5), a result which agrees with the finding by Hering and Morel that competition by Ca2+ was nearly negligible under the experimental conditions employed. It is informative to examine the system in more detail, by performing calculations using different values of PKMHA and pKMHg for Ca2+. As shown in Figure 5, PKMHB is the more critical parameter. If it is set at 7.1, the mean value from Table 11, a substantial competition effect by the alkaline earth cation is predicted, quite different from the observations. It is found that the larger is the assumed value of PKMHB, Le., the weaker is calcium binding at the type B sites, the less competition is predicted. Variations in PKMHA have much less effect. Constraints from Competition Results The above findings suggest that reconsideration of the other results for alkaline earth binding and competition is warranted. It has already been noted that the optimized values of pKMHg are in most cases poorly defined, which suggests that acceptable data fits could be obtained over 524
Envlron. Scl. Technoi., Voi. 27, No. 3, 1993
a substantially wider range of values of this parameter than of pKIf so, it may be possible to obtain pairs of values of PKMHA and PKMHB that explain satisfactorily the data referred to in Tables I1 and 111, while at the same time accommodating the constraining requirement from the Hering-Morel (8) data that PKMHB be quite large. To explore this possibility, all the data sets were reanalyzed, first with P K M for ~ both Ca and Mg fixed at 9.0, a value sufficiently large that there is little predicted calciumcopper competition under the conditions of the HeringMorel experiment. Acceptable fits were obtained in all cases except one, the Cabaniss-Shuman data set CACuMg. With pKfor Mg fixed at 9.0, minimization of residuals in p[Cu] for the CACuMg set required a PKMHA value for Mg of ca. 0.2, which is unacceptably lower than other estimates of this parameter (Table 11). This affords another constraint to the assignment of parameter values. Further calculations on data set CACuMg revealed that more reasonable values of PKMHA could be obtained if, within the model, the binding of Cu(OH)*by the fulvic acid was prohibited, and the PKMHB value for Mg was reduced to 8.5, making Mg binding to type B sites slightly stronger. With these adjustments, a PKMHA of 1.61 for Mg was obtained, which is much closer to the values of Table 11. Furthermore, almost as good a fit was obtained if PKMHA for the alkaline earth was fixed at 2.2 (the overall average value; see below) and pKmaintained at 8.5; with these restrictions, the optimized PKMHA and PKMHB values for Cu (Table V) were still in acceptable agreement with those estimated from the results of direct binding studies (5). It thus emerges that a P K M H B of 8.5 allows acceptable fits of the data sets to be achieved, while being sufficiently high to ensure that competition under the conditions of the Hering-Morel experiment is weak (Figure 5). Except for data set CACuMg, binding of CU(OH)~ by the humic matter is inconsequential, pH values being too low in all cases for significant formation of this species to occur. Therefore the assumption that this species does not bind has relevance only to the CACuMg data set. In view of the above, it was decided to fix pKfor the alkaline earths at 8.5, and the data sets were analyzed once more to fiid values of pKm (Tables IV and V). In most cases, the fixing of PKMHB makes little difference to the goodness of fit [root mean squared error (rmse) value]. In three cases (DA2Ca, MSCa, TACa), the fits are significantly worse, but for all of these the original fit was very good, and so the refits are still acceptable. In the case of the TACa data set, which refers to an acid-base titration, the worsening of the fit is almost entirely due to the increased residual in the highest pH point in a set of only 13 data points. On the basis of the preceding analysis, it seems reasonable to take a value of 8.5 as the best overall or rep-
Table V. Reanalysis of the Data of Table I11 for Competition between Copper and Alkaline Earth Cations’ BACuCa
CACuMg
MACuCa
PKMHA(CU) 1.63 (0.01) pKMHB(Cu) 4.38 (0.03) pKMHA(AE) 2.95 (0.05)
0.99 (0.09) 3.21 (0.21) 2.23 (0.19)
1-10 3.24 1.61
pKMHB(AE) [8.50 fixed]
[8.50 fixed]
L8.50 fixed]
rmse
0.01
Case 6: I=0.5M
Case A: I=0.003M
0.91 3.58 [2.20
fixed] 0.14
0.13
0.14
For all three data sets, PKMHB for the alkaline earth was fixed at 8.5. For data set CACuMg, an optimization was also performed with PKMHA for the alkaline earth fixed at 2.2. The jackknife technique was unsuccessful with data set CACuMg, because the parameter values were too sensitive to the omissions of single data points (see Data Fitting and Constraints from Competition Results). (I
resentative value of pKand to adopt the average value of 2.2 (Tables IV and V) for PKMHA. These assignments have arisen first from fitting of data sets involving only one specifically binding metal and second from the additional constraints due to the Cabaniss-Shuman (7)and Hering-Morel (8) competition results.
Illustrative Calculations It is instructive to explore the performance of model V in its prediction of competition in greater detail by considering pH and ionic strength effects and the contributions of the individual binding sites (including nonspecific counterion accumulation) to the overall amounts bound. To do this, the interactions of trace amounts of copper and cadmium with fulvic-type material under conditions of low and high ionic strength are considered. These two metals are chosen because parameter values have been estimated from several fairly extensive data sets (5). The mean values of PKMHA and PKMHB for copper species [Cu2+, Cu(OH)+]are 0.8 and 3.7, respectively, while for Cd2+they are 1.5 and 5.5. Copper represents relatively strongly bound species (Cu2+,Pb2+,V02+),while cadmium is typical of a group of metal ions (Cd2+,Ni2+, Zn2+, Co2+)with moderate affinities for humic substances. Case A represents freshwater, with an ionic strength of 0.003 M. Two solutions are considered, the first being 0.003 M with respect to a monovalent cation that does not bind at the discrete humic sites, and the second being 0.001 M in AE2+. Case B represents seawater, with an ionic strength of 0.5 M. The first solution of this pair is 0.5 M with respect to a monovalent cation; the second is 0.35 M with respect to the monovalent cation and 0.05 M with respect to AE2+. In order to focus attention on the binding behavior of the humic substances, no account is taken of complexation reactions of the trace metals with inorganic ligands other than OH- (e.g., C032-and C1-). The total concentration of each trace metal is set at lo-* M (i.e., 1 pg L-l), and the concentration of “average” fulvic acid is set at 5 mg L-l. Figure 6 shows plots of metal binding as a function of pH. Examination of Figure 6 shows that, as is generally expected for weak acids, metal-binding strength increases with pH. It is also apparent that binding is weaker at the higher ionic strength. To some extent, this reflects the different solution activities of the trace metal ions at the two ionic strengths, the activity coefficients being 0.76 and 0.13 in the low and high ionic strength solutions, respectively. More important, however, is the influence of ionic strength on the discrete humic sites. Within model V, this is described with the expression exp(-2wzZ), as explained above. For example, at a net
-
II ’
4
5
6
7
8
9
4
I
,/--
5
6
7
8
9
PH Flgure 6. Binding of copper (Cu2+, CuOH*+) and &I2+ by fulvlc-type material at low and high ionlc strengths and In the presence (- -) and absence (-) of Ca2+,calculated wlth model V. The total concentration of the trace metals is lo-’ M throughout.
-
humic charge (Z)of -3 X equiv g-l, and an ionic strength of 0.003 M, the value of exp(-2wzZ) is 22.6, which is the factor by which electrostatic attraction enhances the affinity of the humic molecules for a divalent ion, compared to binding at zero humic charge. At an ionic strength of 0.5 M on the other hand, the expression is equal to only 1.2, so that there is very little electrostatic enhancement of binding. The importance of the electrostatic effect is also evident from the calculated AE binding, which occurs to a lesser extent at the higher ionic strength (case B), despite the 50-fold greater concentration of AE2+. This explains why there is a greater competitive effect due to AE2+in case A than in case B. The alkaline earth cation is calculated to compete much more effectively with cadmium than with copper (Figure 61, simply because the latter binds more strongly. The greatest competition occurs at pH values in the region 5-6, which is where the type A sites are most significant in metal binding. At higher pH values, the type B sites assume greater importance, and as has been concluded from the Hering-Morel data, AE2+binding at these sites is weak. Within model V there are effectively 21 different binding sites for metals, these being the 8 monodentate sites, the 12 bidentate sites, and the diffuse layer counterion accumulation. Tables VI and VI1 show how the different discrete sites, and the diffuse layer, contribute to the Envlron. Scl. Technol., Vol. 27, No. 3, 1993 525
Table VI. Calculated Distributions of Copper and Cadmium among Fulvic Acid Binding Sites: Case An [CUI MON(1) MON(2) MON(3) MON(4) MON(5) MON(6) MON(7) MON(8) MON-tot BID(1,P) BID(1,4) BID(1,G) BID(1,8) BID(2,3) BID(2,5) BID(2,7) BID (3,4) BID(3,6) BID(3,8) BID(4,5) BID(4,7) BID-tot
DDL total -2 [MI,
[Cdl
(-1
(+)
(-)
(+)
2.16 x 10-14 2.81 x 10-13 3.62 x 10-l2 4.32 X lo-" 2.77 x 10-13 3.09 x 10-13 3.09 x 10-13 3.09 x 10-13 4.83 X lo-" 2.89 x 10-13 4.44 x 10-11 6.35 x 10-13 6.36 x 10-13 4.83 x lo-" 7.39 x 10-12 8.25 X 7.22 x 10-9 1.06 X 1.06 X 1.13 x 10-9 1.27 x 10-9 9.94 x 10-9 2.83 x 10-13 9.99 x 10-9 4.67 x 10-3 1.19 x 10-11
2.91 x 10-14 3.66 x 10-13 3.31 X 8.71 X 9.15 x 10-13 1.22 x 10-12 1.23 x 1.23 x 10-l2 1.70 x lo-" 3.86 x 10-13 2.55 X lo-" 2.51 X 2.53 X 2.58 X lo-" 2.44 X lo-" 3.28 X lo-" 4.23 x lo-'] 4.21 X 4.23 X 3.81 x 10-9 5.04 x 10-9 9.85 x 10-9 7.84 x 10-13 9.87 x 10-9 2.59 x 10-3 1.33 X
1.35 x 10-13 1.76 X 2.27 x 2.70 X 1.38 x 10-13 1.54 x 1 0 4 3 1.54 x 10-13 1.54 x 10-13 2.96 x 3.60 x 1 0 4 3 5.54 x 10-11 6.30 x 10-14 6.31 x 1 0 4 4 6.03 X lo-" 7.33 x 10-13 8.18 x 10-13 9.02 X lo* 1.05 X 1.06 X lo-'] 1.13 X 1.26 X 9.40 x 10-9 8.51 X 9.70 x 10-9 4.67 x 10-3 3.05 X
3.83 x 10-13 4.81 X 4.35 x 10-11 1.15 X 9.57 x 10-13 1.28 X 1.28 X 1.28 x 1.68 X 1.01 x 10-12 6.68 X lo-" 5.24 x 10-13 5.27 x 10-13 6.76 X lo-" 5.09 X 6.83 X 1.11x 10-10 8.77 X lo-" 8.81 X 10'" 7.95 x 10-10 1.05 x 10-9 2.28 x 10-9 4.86 x lo-" 2.50 x 10-9 2.59 x 10-3 7.50 x 10-9
VCa
2.04 X 2.56 x 2.32 x 6.10 x 2.55 X 3.41 X 3.42 X 3.42 x 8.69 x 1.08 X 7.09 x 2.79 x 2.80 x 7.18 X 2.71 X 3.64 X 1.18 x 4.66 x 4.69 x 4.23 X 5.59 x 2.72 x 1.30 X 2.44 x 2.59 x 1.00 x
lo4
10-5 10-4 10-4 lo-@ lo-@
10-4 lo+ 10-9 10-9 10-5 IO-@
lo-@ 10-4 10-7 10-7 10% 10+ 10-4 lo-? 10-3 10-3 10-3
"The calculations refer to pH 7, I = 0.003 M, with total concentrations of Cu2+and Cd2+of M, and a total fulvic acid concentration of 5 mg L-I, in the absence and presence of 0.001 M Ca2+,denoted by (-) and (+), respectively. Results for the trace metals are expressed in molar concentrations. See Model Description for explanation of site nomenclature. Binding due to counterion accumulation in the diffuse part of the electrical double layer is indicated by DDL. The net humic charge (equiv g-l) is denoted by 2, and the free metal concentrations by [MIf.
Table VII. Calculated Distributions of Copper and Cadmium among Fulvic Acid Binding Sites: Case B" [CUI MON(1) MON(2) MON(3) MON(4) MON(5) MON(6) MON(7) MON(8)
MON-tot BID(1,2) BID(1,4) BID(1,6) BID(1,8) BID(2,3) BID(2,5) BID(2,7) BID(3,4) BID(3,6) BID(3,8) BID(4,5) BID(4,7) BID-tot DDL total -2 [MI,
7.43 x 9.65 x 1.25 X 1.61 X 4-48 x 8.69 x 8.81 x 8.81 x 2.05 X 9.91 x 1.65 X 1.79 X 1.81 X 1.67 X 1.20 x 2.35 X 2.76 x 3.00 X 3.05 X 1.98 x 3.89 x 9.31 x 1.35 x 9.33 x 5.02 x 6.68 X
ICdI (+)
(-)
10-'5 10-14 lo-" 1043
10-13 10-13 10-13 lo-" 10-14 lo-'] lo-" lo-" lo-" 10-9
10-9 10-9 10-9 10-13 10-9 10-3
1.03 x 1.27 x 1.01 x 2.20 x 6.70 x 1.40 X 1.43 X 1.43 X 8.28 X 1.36 x 7.07 X 2.89 X 2.93 X 7.09 X 1.79 X 3.80 X 1.02 x 4.77 x 4.84 X 2.66 x 5.05 x 8.76 x 5.23 x 8.77 x 2.49 x 1.23 x
10-14 10-13 10-12 10-12 10-13
1043
lo-'* lo-" lo-" 10-11 10-10 10-9 10-9 10-9 1044
10-9 10-3 10-9
(+)
(-)
1.72 x 2.24 x 2.90 X 3.73 x 8.26 x 1.60 x 1.62 x 1.62 x
10-14 10-13
4.10 X 4.59 x 7.64 X 6.56 x 6.66 X 7.72 x 4.39 x 8.64 x 1-28 x 1.10 x 1.12 x 7.30 X 1.43 X 1.53 x 1.86 X 1.58 x 5.02 x 8.42 x
10-l' 10-14
10-1' 10-14 1043
1043
10-13
10-14 10-l2 10-13 10-13 10-9 10-1' 10-11
lo-"
10-9 10-9 10-3 10-9
"The calculations refer to pH 7, Z = 0.5 M, with total concentrations of Cu2+and Cd2+of
1.46 x 1.80 x 1.44 X 3.13 X 7.57 x 1.59 x 1.61 x 1.61 x 5.32 X 3.84 x 2.01 x 6.51 x 6.61 x 2.01 x 4.03 x 8-57 x 2.89 X 1.07 X 1.09 x 6.00 X 1.14 X 2.04 X 4.42 x 2.10 x 2.49 x 9.79 x
10-14 10-13 1O-I'
10-14 10-13 10-13 10-13 10-14 10-12 10-14 10-14 10-12
10-13 10-13 lo-" 10-11
lo-"
10-13
10-10 10-3 10-9
Environ. Scl. Technol., Vol. 27, No. 3, 1993
2.98 X 3.68 x 2.95 x 6-39 x 7.75 x 1.62 x 1.65 x 1.65 X 9.74 x 1.57 X 8.18 x 1.33 X 1.35 X 8.20 x 8.23 X 1.75 x 1.18 x 2.19 X 2.23 X 1.23 x 2.32 x 3.23 x 4.53 x 1.75 x 2.49 x 5.00 X
10% 10-5 10-4 10-4 10-8 10-7 10-7 lo-' 10-4
lo4 10-5 lo-@
10-5 10-7 10-4
10%
lo4
10-5 10-5 10-4 10-4 10-3 10-3
lo-'
M, and a total fulvic acid concentration of
5 mg L-l, in the absence and presence of 0.05 M Ca2+,denoted by (-) and (+), respectively. Details as for Table VI.
528
YCa
Table VIII. Illustration of the Indirect Competitive Effect, Due to a Decrease in Net Humic Charge, zh [CUI BID (3,4) BID(4,5) BID(4,7) -2
[Cdl (-)
(-)
(+)8.5
(+)IC0
6.79 X 1.17 X 1.30 X 4.65 x 10-3
4.01 X lo-” 3.69 x 10-9 4.79 x 10-9 2.59 x 10-3
4.01 X 3.77 x 10-9 5.05 x 10-9 2.60 x 10-3
2.63 x 3.59 x 4.00 X 4.65 x
10-9 10-11 10-l’ 10-3
(+)8.5
(+)IO
1.48 X 1.06 X lo-“ 1.40 X 10‘” 2.59 x 10-3
1.48 X 1.11 x 10-11 1.48 X lo-“ 2.60 x 10-3
M Ca2+. The free trace metal concentrations are fixed at Calculations refer to case A; pH 7, Z = 0.003 M, with (+) and without (-) M, and the concentration of “average”fulvic acid is 5 mg L-I. The value of PKMH, for CaZ+was fixed at 2.2, while the value of PKMHB was set at both 8.5 and 100, denoted by (+)8.5 and respectively; the setting of PKMHBto 100 effectively abolishes binding at monodentate type B sites, and at bidentate sites that include a type B site. Concentrations of trace metal bound at the three major bidentate sites are shown.
binding of the trace metal cations and AE2+at neutral pH. For the trace metals, binding takes place almost exclusively at bidentate sites, at both low and high ionic strengths. However, the concentrations of AE2+,and its PKMHAand PKMHB values, are such that this cation binds mostly at the monodentate and diffuse double-layer (DDL) sites. This is important with respect to competition, because it means that the trace metals and the alkaline earth are substantially separated in their binding behaviors, so that to a considerable degree they are not competing for the same sites. With regard to the individual sites, it is seen from Tables VI and VI1 that bidentate sites (3,4), (4,5), and (4,7) contribute most to trace metal binding. The competitive effects of AE2+are much greater at bidentate site (3,4) than at the other two, because of the substantial difference in strengths of binding of AE2+by type A and type B sites. This can be illustrated by considering the pKm values for the exchange of a metal species for two protons at the bidentate sites, bearing in mind that the smaller the pKm the greater the strength of binding. For example, the pKMHvalue for copper binding at site (3,4) is 1.6 and that of AE2+is 4.4. The difference between the values for the two metals is sufficiently small that an excesa of AE2+gives appreciable competition, and as a result, binding at BID(3,4) is substantially diminished by competition with AE2+ (Tables VI and VII). In contrast, the corresponding pKm values for site (4,5) are 4.5 for copper but only 10.7 for AE2+,so that a very great excess of AE2+would be required to exert a significant competitive effect. Indeed, in the examples of Tables VI and VII, the displacement of copper from site (3,4) causes such an increase in the solution activity of copper that there are calculated to be increases in binding at BID(4,5) and BID(4,7). For cadmium in case A, the same effect occurs, but at the higher ionic strength (case B), the increases in binding at sites (4,5) and (4,7) are much less significant, due to the weaker affinities of the discrete type B sites for Cd2+ and the lack of an electrostatic enhancement of binding strength. Because the calculated results in Tables VI and W refer to a fixed total concentration of trace metal, they obscure a secondary competitive effect by AE2+which arises because the relatively strong binding of AE2+to monodentate type A sites, or to bidentate sites comprising pairs of type A sites, causes a reduction in the net humic negative charge. Because model V embodies the assumption that the humic charge is effectively averaged over the whole molecular surface, the overall electrostatic attraction for the trace metal cations at all the discrete sites is diminished, and binding at monodentate type B sites, or bidentate sites involving type B sites, is weakened indirectly. This can be illustrated by performing calculations for fixed free trace metal concentrations. As shown in Table VIII, under these circumstances binding at all three of the major
bidentate sites is less in the presence of AE2+. That the decreases in binding at BID(4,5) and BID(4,7) are due almost entirely to the indirect electrostatic effect is evident from the nearly identical results obtained when pKfor AE2+is set to 100, which effectively prevents the binding of AE2+at bidentate sites involving type B proton sites. In principle, AE2+competes with the trace metals for nonspecific binding (counterion accumulation). However, for the two examples considered, such nonspecific bindmg is unimportant for the trace metals (Tables VI and VII), and so the displacements by the alkaline earth cation are insignificant. Competition of this kind will be of greater importance at lower ionic strengths, for cations with lower affinities for the discrete binding sites, and/or for cations of higher charge. Concluding Remarks The results of the present study exemplify the view of Hering and Morel (8)that “data on interactions of humic acids with several metals and particularly on competitive interactions serve to constrain models of metal-humate interactions”. Consideration of competition effects has helped in the estimation of the key model V parameters for metal binding-pKMm and pKMHB-from data which only allow the first to be well-defined. Indeed, the results of Hering and Morel’s own study are the most telling in this respect. With the realization that weak calcium binding by the type B sites can be accommodated within all the available data sets, it is possible to account quantitatively for all the observed competition effects (6-9), while maintaining acceptable fits for the data sets from simple binding studies. However, the general applicability of the model is maintained only by making the assumption that CU(OH)~ binding by humic matter does not occur, in order to explain the high pH results of Cabaniss and Shuman (7). There are three particular features of model V that allow it to deal with the observed competition effects: (a) the presence of two groups of sites (A and B), which can have different relative affinities for different metals; (b) the presence of both monodentate and bidentate sites, which allows the creation of a few “high-affinity” sites favored by the trace metals, together with a large number of weaker sites which can accommodate alkaline earth cations; (c) the possibility of binding by nonspecific accumulation of counterions in the diffuse layer, which also diverts the alkaline earth cations from binding at the bidentate sites. In this context, it is of interest to compare model V with other current models of ion binding by humic substances. Hering and Morel (8) established that although a simple model having three discrete metal-binding sites could account very well for copper and calcium binding considered separately, it markedly overestimated the competitive influence of calcium on copper binding. Whether this Environ. Sci. Technol., Vol. 27, No. 3, 1993 527
difficulty would be overcome by models that postulate a continuum of binding sites (12,14, 15) is unclear. Such models deal with competition by assuming that the distributions of equilibrium constants for binding parallel one another, i.e., the distributions have the same shape but different central values, and although this approach has met with success in describing the influences of pH and it remains to be aluminum on europium binding (14,15), seen whether the competitive influence of alkaline earths could be described. The model of Bartschat et al. (13) considers the molecular size dependence of the electrostatic influence on binding, and it is conceivable that this would provide the flexibility required to account for competition by the alkaline earths. With regard to the importance of counterion binding, identified in the present work, there seems to be no reason, at least in principle, why such nonspecific binding could not be introduced into any model that allows the calculation of net humic charge. An obvious possibility for the further testing of model V is the measurement of cadmium binding as a function of alkaline earth concentration, and comparison of the results with the predictions of Figure 6 and Tables VI and VII. Study of competition effects with copper at low pH would also be informative. More generally, there is a need for a comprehensive set of experiments-proton and metal binding, and competition studies, over a wide range of conditions-to be performed on a single humic sample, since this would remove the influence of variability among preparations and thereby permit better evaluation of model V and other models. Acknowledgments Thanks are due to M. A. Hurley for helpful discussions and to two anonymous reviewers for their perceptive and constructive criticisms. Appendix: Algebra of Model V The contents of binding sites, in moles per gram of humic substance, are given in terms of the adjustable parameter nAand the proximity factor fpr. The subscript H refers to proton binding, MON and BID refer to monodentate and bidentate binding of metals. for i = 1-4 nH(i) = nA/4 i
(AI)
P K M H ( ~=J PKMHAO') for i = 5-8
(A2)
for i = 1-8 nMoN(i) = (1 - fp,)nH(i)
(A31
for i = 1-12 nBID(i) = fprn~/16
(A4)
The intrinsic proton dissociation equilibrium constanta are calculated from PKA, pKB, APKA,and APKB: for i = 1-4
(-47)
PKMH(ij) = PKMHBO') (A8) The electrostatic interaction factor (w) is given in terms of the parameter P and ionic strength I; w = P log I (A9 The volume of diffuse layer in liters per gram of humic substance is given in terms of Avogadro's number ( N ) , humic radius (r),molecular weight ( M ) , and the DebyeHuckel characteristic distance ( l / ~ ) :
Calculation of the amounts of ions bound per gram of humic substances requires input values of ionic strength (I)and activities (a) of the ions in question. First, it is necessary to compute the fractional occupancies by protons of metal-free sites: 1 f(i) = (All) 1 + (Kdi) exp(2wZ)/a~) When binding site occupancies by metals and net charge are calculated, sites are denoted by i, j , and k , and metal species by 1. Fractional occupations of monodentate sites are given by OMONG,~) KMH(i,l) exp(241 - z(l)JZ) f(i)a(O/aH N (AW 1 + Z K d i , O exp(2w{l- z(l)JZ) f(i)a(l)/aH 1=1
Fractional occupations of bidentate sites i, comprising proton-binding sites j and k , are given by OBID(i,l) = (KMHO',l)KMH(k,l)exP(2W{2N
z ( l ) l z ) fO') f ( k ) a ~ ( l ) / a ~ ~ )+/ (CKMHO',1)KMH(k,l) l x 1=1
expW12 - z ( W ) fO') f ( k b ~ ( O / a ~ '(A131 ) Complexed metal (moles bound per gram of humic substance) is calculated as 8
12
1=1
1=1
vC(l) = ZnMON(i)OMON(i,l) + xnBX)(i)flBID(i,l)
for i = 5-8 nH(i) = n ~ / 8
for i = 1-4
(A14)
The net humic charge (2) is obtained by summing the charges at the monodentate and bidentate sites:
N
ZBID(i) = nBID(i)(-2
+ (1=1 x h l ( i , ~ ) z ( ~+) ({2fG)f(k) ) t' N
fW[1 - f ( k ) l + f(k)[l - f0')11(1 - x h ~ ( i , O )(A16) )) 1=1
8
12
for i = 5-8
z= iZzModi) + EzBID(i) =l ill
Intrinsic equilibrium constants for metal-proton exchange, for metal j , are given by PKMHA and PKMHB:
The value of Z is nearly always negative, and therefore counterions are cations. Total concentrations of cations of charge j in the solution phase (S) and diffuse layer (D) are given by the sums of the concentrations of individual cations [e&), c&)] of charge z(i):
528
Environ. Scl. Technol., Vol. 27, No. 3, 1993
(A171
N
cjs
C
N
cjD =
CS(~)
C
i=l z(i)=j
i-1 r(i)=j
cD(i)
(A181
The ratio of diffuse layer concentration to bulk solution concentration for cations of charge j is given by Donnantype expressions: C j ~ / C j s = Ri (AN) This enables the balance between net humic charge (2) and the counterions (charge +1 to +4) to be established: 4
Z = -VDCcjSR’ j=l
.
(A201
and the concentration of the individual species i in the diffuse layer can be calculated from the bulk solution concentration: cD(i) cjDcS(i)/cjS (Am Therefore, the moles of species i bound in the diffuse layer, per gram of humic substance, can be obtained vD(i) = CD(i)vD (A221 The total bound metal (complexed and accumulated as counterions), per gram of humic substance, is given by V(i) = Yc(i) + YD(i) (AB) Literature Cited (1) Buffle, J. In Metal Ions in Biological Systems. Circulation of Metals in the Environment; Sigel, H., Ed.; Dekker: New York, 1984; Vol. 18. (2) Boggs, S.; Livermore, D. G.; Seitz, M. G. Rev. Macromol. Chem. Phys. 1985, C25, 599-657. (3) Sposito, G. CRC Crit. Rev. Enuiron. Control 1986, 16, 193-229. (4) Weber, J. H. In Humic Substances and Their Role in the Environment; Frimmel, F., Christman, R. F., Eds.; Wiley: Chichester, England, 1988. (5) Tipping, E.; Hurley, M. A. Geochim. Cosmochim. Acta 1992, 56,3627-3641. ( 6 ) Buffle, J.; Deladoey, P.; Greter, F. L.; Haerdi, W. Anal. Chim. Acta 1980, 116, 255-274.
(7) Cabaniss, S. E.; Shuman, M. S. Geochim. Cosmochim. Acta 1988,52, 185-193. (8) Hering, J. G.; Morel, F. M. M. Environ. Sci. Technol. 1988, 22, 1234-1237. (9) McKnight, D. M.; Wershaw, R. L. Humic Substances in the Suwannee River, Georgia: Interactions, Properties, and Proposed Structures. Open-File Rep.-US. Geol. Serv. 1989, NO.87-557. (10) Marinsky, J. A.; Ephraim, J. Environ. Sci. Technol. 1986, 20,349-354. (11) Ephraim, J.; Alegnet, S.; Mathuthu, A.; Bicking, M.; Malcolm, R. L.; Marinsky, J. A. Environ. Sci. Technol. 1988, 20, 354-366. (12) De Wit, J. C. M.; Van Riemsdijk, W. H.; Nederlof, M. M.; Kinniburgh, D. G.; Koopal, L. K. Anal. Chim. Acta 1990, 232, 189-207. (13) Barbchat, B. M.; Cabaniss, S. E.; Morel, F. M. M. Environ. Sci. Technol. 1992, 26, 284-294. (14) Susetyo, W.; Dobbs, J. C.; Carreira, L. A.; Azarraga, L. V.; Grimm, D. M. Anal. Chem. 1990,62, 1215-1221. (15) Dobbs, J. C.; Susetyo, W.; Knight, F. E.; Castles, M. A.; Carreira, L. A.; Azarraga, L. V. Int. J.Environ. Anal. Chem. 1989, 37, 1-17. (16) Perdue, E. M.; Lytle, In Aquatic and Terrestrial Humic Materials; Christman, R. F., Gjessing, E. T., Eds.; Ann Arbor Science: Ann Arbor. MI. 1983. (17) Tipping, E.; Backes, C. A.; Hurley, M. A. Water Res. 1988, 22, 597-611. (18) Nash, J. C.; Walker-Smith, M. Nonlinear Parameter Estimation. An Integrated System in BASIC; Dekker: New York, 1987. (19) Reed, W. J. Biometrics 1983, 39, 987-998. (20) Dempsey, B. A. Ph.D. Thesis, Johns Hopkins University, 1981. (21) Marinsky, J. A.; Reddy, M. M.; Ephraim, J. H.; Mathuthu, A. Manuscript in preparation. (22) Schnitzer, M.; Skinner, S. I. M. Soil Sci. 1966,103,247-252. (23) Mathuthu, A. P b D . Thesis, State University of New York a t Buffalo, 1987.
Received for review June 15,1992. Revised manuscript received October 6,1992. Accepted November 17,1992. This work was funded by the U.K.Department of the Environment. The results will be used in the formulation of Government Policy, but views expressed in this paper do not necessarily represent Government Policy.
Environ. Sci. Technol., Vol. 27, No. 3, 1993 529
