Trace metals in contaminated waters Several models are used to predict the behavior of soluble metals in natural waters contaminated by municipal sewage and sludge
Garrison Sposito Department of Soil and Environmental Sciences University of California Riverside, Calif. 92521
Contamination of natural waters by municipal sewage effluents and sludges brings with it the possibility that the concentrations of soluble trace metals in the waters may increase to potentially hazardous levels ( l - j ) , Disposing of treated municipal sewage (either efflueqt or sludge) on land and in the ocean thus poses an environmental management problem whose solution depends on the development of sound information concerning the behavior of trace metals in aqueous phases significantly perturbed by the intrusion of organic compounds of anthropogenic origin. Given the wide variation in composition of both treated municipal sewage and natural waters themselves (oceans, lakes, rivers, pore waters in sediments, soil water, groundwater), a detailed understanding of soluble trace metal behavior in their admixtures seems impossible to achieve within the time frame of interest to environmental management. The practical alternative is to identify the essential aspects of trace metal reactions with respect to the expected hazards associated with their presence in sewage-natural water mixtures with the aid of simplified but quantitative models. The partitioning of trace metals into chemical forms in surface and subsurface waters mixed with treated municipal sewage poses a complicated problem involving complexation, adsorption, coagulation, oxidation-reduction (redox), and biological phe396
Environmental Science & Technology
nomena with both equilibrium and kinetic features ( 4 ) .The present article will make no attempt to consider trace metal speciation in this most general context, but instead will focus solely on the developmental physical chemistry of specific models related to the complexes of trace metal cations with the soluble organic ligands in sewage sludges and effluents under oxic conditions. Since complexation reactions in natural water usually are quite rapid when they do not involve redox phenomena, it is reasonable to focus on equilibrium chemical models of trace metal complexes, even when sewage compounds are involved. In the broadest picture, trace metal complexation rCactions in contaminated natural waters lead to a dense web of chemical interrelations which are mediated by variable fluxes of matter and energy from the biosphere, hydrosphere, lithosphere, and atmosphere. Despite the obvious kinetic considerations these variable fluxes bring to mind, particularly with regard to the labile nature of the organic compounds in treated sewage ( 5 , 6), an equilibrium model still can be of great value in establishing trends for given environmental conditions. Useful quantitative predictions can often be made without interfacing an equilibrium chemical model and biological or hydrological models ( 5 ) . Toxicity and complexation The principal environmental concern over elevated concentrations of trace metals, such as Al, Cr, Ni, Cu, Zn, Cd, Hg, and Pb, in natural waters relates to toxicity. From an ecological perspective, this concern would be aimed initially toward problems of toxicity to aquatic organisms and to higher plants grown in soil. For a response to these concerns, it
appears that two broad generalizations based on the principles of coordination chemistry are directly relevant. The first states that the greater its degree of Class b character ( 7 , 8 ) , the more harmful a trace metal will be to an organism. Class b character includes the properties of large ionic size and polarizability, low oxidation state and electronegativity, and large affinity for sulfide ions and organic sulfur moieties. This single criterion for relative toxicity is sufficient to establish toxicity sequences for the trace metals. Among the eight metals mentioned above, the general toxicity ordering would be ( 7 ) : Hg(I1) > Cu(I1) > Pb(I1) > Cd(I1) > Cr(II1) > Zn(I1) > Ni(I1) > Al(II1). The exact ordering will vary somewhat among organisms, but the general pattern is always evident. The second generalization relates directly to the toxicity of soluble trace metal cations and states that metal speciation is more significant than total metal concentration in a natural water system. A growing body of literature suggests that, among the more harmful trace metals, there are definite patterns in the data on toxic effects when these data are related to the chemical forms of the metals in aqueous solution ( 9 , 10). The general rule emerging from many studies is that strongly complexed forms of a trace metal are intrinsically less toxic than weakly complexed or free ionic forms (9,lO). In other words, the more strongly a metal is complexed, the lower is the toxic effect of a given total metal concentration. Since it is well known that metals having a high degree of Class b character tend to form their strongest complexes through large decreases in enthalpy mediated by covalent interactions ( 11 ), the proposed inverse re-
0013-936X/81/0915-0396$01.25/0 @ 1981 American Chemical Society
lationship between toxicity and complexation may contribute directly to a chemical basis for the management of natural waters contaminated with the more harmful trace metals. The ramifications of these qualitative, general concepts for the development of specific chemical models of trace metal complexation in treated sewage-natural water mixtures are not difficult to perceive. Useful predictions can be obtained from models which take into account the multiplicity of possible complexes of the trace metals of interest, especially complexes with the soluble organic fraction of treated sewage. Thus the primary objective of these models should be to give an accurate description of the functional group chemistry of the sewage insofar as it relates to the formation of trace metal complexes. A more detailed, structural description of the chemical properties of sewage is always desirable, but to be useful, it must be related in a quantitative manner to the complexation reactions of the functional groups. Organic functional groups
Chemical models of two quite different types have been employed to describe quantitatively the reactions between potentially hazardous trace metal cations and the soluble organic fraction of treated municipal sewage. One of these models has the attribute of broad applicability under a variety of natural water conditions, whereas the other has the advantage of directly incorporating laboratory data on trace metal-sewage complexes. Neither model attempts to do more than account for the organic functional group chemistry of treated sewage on a macroscopic level. In particular, no consideration is given to describing the molecular structure of the organic fraction of sewage. The first class consists of mixture models, which are sets of organic acids whose reactions with trace metal cations are well characterized and whose functional groups are known to exist also in the soluble organic fraction of treated sewage. The quantitative distribution of organic acids in the model is determined by the organic carbon concentration in the sewage-natural water system to be modeled and by any other available data pertinent to the functional group chemistry of the sewage. Table I gives two recent examples of mixture models. The Westall et al. (MWOM) model ( 1 2 ) comprises six organic acids which were selected on the basis of analytical data to describe
the soluble organic fraction of primary-treatment Los Angeles County sewage. The concentrations of the six acids (expressed in the table as negative common logarithms of the total molar concentrations) were determined by the condition that each acid contribute an identical molar concentration of carbon to the total molar concentration of organic carbon in the sewage (6 X M). The Mattigod and Sposito (MS) model ( 1 3 ) comprises aliphatic, aromatic, and amino acids that were selected on the basis of analytical data to describe the fulvic acid fraction of sewage sludge from a treatment plant in Rialto, Calif. (Fulvic acid is the alkali-extractable fraction that is soluble in dilute, inorganic acid ( I d ) . ) The distribution of the nine organic acids in this model was not uniform, but was arranged to make the calculated proton titration curve of the mixture simulate the measured proton titration curve of a solution containing Rialto sludge fulvic acid at a concentration of 0.5 kg/m3, which is typical for the aqueous phases of soils receiving sewage sludge as an amendment. The basic assumption underlying the use of a mixture model is that the measured thermodynamic stability constants for trace metal complexes with the chosen set of organic acids will combine to closely approximate the conditional stability constants for trace metal complexeswith the organic fraction of treated sewage. The soundness of this premise clearly improves as the extent to which a mixture model has been calibrated against data on trace metal-sewage reactions increases. But the direct laboratoryvalidation of a mixture model will generally be difficult (15). with the result that the model will tend to be evalu-
ated more by its ability to make correct predictions than by its intrinsic chemical semblance to fact. On the other hand, mixture models have several attractive features that may outweigh their usual lack of direct validation. They are useful over a wide range of pH values and ionic strengths: they are easy to incorporate into computer programs; and they do not require the modeler to measure stability constants in order to apply them to a sewage-natural water system. Quasiparticle models
The second class of models of the organic functional groups in treated sewage are the quasiparticle models. A quasiparticle model is a mathematical description of an aqueous solution of sewage in which the actual assembly of organic compounds is replaced by an assembly of hypothetical, identical macromolecules whose mole mass is the number-average mole mass of the actual mixture and whose trace metal complexation reactions closely mimic those in the real system. These hypothetical macromolecules are called “quasiparticles” because they are only theoretical constructs, not real molecules. They are introduced because the mathematical description of their complexation reactions is far less complicated than that of the reactions in the sewage mixture considered individually a t the molecular level. The basic premise of the quasiparticle model is that, although the soluble organic fraction of treated sewage contains molecules exhibiting a wide range in chemical composition, mole mass, and functional group properties, the mixture as a whole will possess average properties that are classifiable and describable in terms of only a few
TABLE I
Two mixture models of the metal-complex groups in the soluble organic fraction of m
Glutamic PMhalic Salicylic
3.8
Phthalic
Lysine Ornithine Valine
Volume 15, Number 4, April I981
as?
macroscopic parameters. For example, with respect to the complexation of protons or trace metal cations, the organic functional groups in treated sewage may fall into just a few classes. Each of these classes is describable, in principle, by a certain maximum number of complexed protons or metal ions and by a single complex stability constant, even though on the molecular level it is probable that in a given class no two complexing functional groups are chemically quite the same. The concept of the quasiparticle originated 75 years ago in a paper by Einstein (16) in which it was shown that some of the properties of electromagnetic radiation could be described in terms of a gas of noninteracting quasiparticles now called “photons.” In the same spirit, the thermodynamic properties of an insulating solid can be described mathematically by replacing the actual solid with a gas of quasiparticles, called “phonons,” and a magnetic solid can be described by replacing it with a gas of “magnons” ( 1 7 ) . Table 2 gives a short list of some of the better-known quasiparticles. In each example, the actual physical system is substituted by an assembly of identical quasiparticles whose mathematical description is simpler than a full theoretical description of the actual system a t the most detailed level would be. A quasiparticle model has been developed to describe the complexation reactions of the fulvic acid fraction of municipal sewage sludge (18, 19). This organic fraction is considered to
TABLE 2
A short lid of models
Insulating crystal Ferromagnetic Mawon crystal Electrons in a
Plasmon
Pbm Electrons in a
conductor Electrons in an insulator Water in porous media Fulvic acid fraction of sewam sludge
Quasielectron Polaron Darcion
Mean fulvic acid unit
398 Environmental Science 8 Technology
include the extractable, water-soluble compounds that are most reactive toward trace metal cations ( 1 4 , 20, 21). Such compounds are likely to play an important role in determining the bioavailability of these cations in natural waters. Fulvic acids extracted from a wide variety of organic materials tend to have similar functional group character (14,20). Thequasiparticleassociated with sewage sludge fulvic acid is known as a mean fuluic acid unit (18). the complexation reactions of which can be described mathematically by a straightforward application of the statistical mechanics of polyfunctional molecules (18.19.22). In this respect, the mean fulvic acid unit is similar to any macromolecule with acidic, metal-complexing functional groups, such as a protein. Protonation reactions The description of the protonation reactions of a mean fulvic acid unit is somewhat complicated by the fact that the units can polymerize through hydrogen bonds (18). However, it turns out that the proton titration curve follows the simple expression:
Here, nH is the number of moles of protons complexed per mole or per kilogram of mean fulvic acid units; RH, is the maximum number of moles of protons that can be complexed by a mole or a kilogram of the ith class of acidic functional groups: cK, is the conditional protonation constant for the ith class of functional groups; and [H+] is the molar concentration of protons. The parameters nHz and e K , in Equation 1 depend on temperature, pressure, and the composition of the fulvic acid-natural water mixture, including the total fulvic acid concentration. A proton titration curve for a fulvic acid extracted from Rialto sewage sludge is shown in Figure 1. It is evident that this curve can be described by just three classes of acidic functional groups. (A fourth class, which titrates at pH values less than three, is only suggested in that illustration.) The line through the data points was calculated with Equation 1 and the following parameters: nHI = 0.614 mol/kg; logeKl = 4.06; n ~ =2 0.797 mol/kg; IOgCK2 = 6.55; nH3 = 0.552 mol/kg, and log%, = 9.295. These six parameters proved sufficient to describe the protonation of the sludge fulvic acid a t a concentration of 1.0 kg/m3 in 0.1 m KCI. At different ionic
strengths and fulvic acid concentrations, Equation I still was found to be applicable, but the values of the nHi employed were different, although the logcKi (i = I, 2, 3) remained essentially the same (18). The complexation of a bivalent metal cation by a mean fulvic acid unit in a perchlorate background medium involves a competition-among the bivalent metal ion, the metal cation in the perchlorate salt, and the protonfor functional groups in the fulvic acid. If the bivalent metal cation is complexed only by unidentate and bidentate ligands in the fulvic acid, then, according to the quasiparticle model, the number of moles of bivalent metal ion complexed per mole of mean fulvic acid units, nM, is given by the expression (19): nM = z i n i ( l ) x M i ( l ) + & .I( 21) x M j ( 2 ) (2)
In Equation 2, ni(’) is the maximum number of moles that can be complexed by the i t h class of unidentate ligands: nj(2)has a similar meaning for the bidentate ligands; xui(l) is the mole fraction of the metal complexed by the ith class of unidentate ligands; and x@ has a similar meaning for the bidentate ligands. Equation 2 can be applied once the parameters x M i ( l ) and X M ~ ( have ~ ) been related to the concentration of the bivalent metal ion, M2+, in the fulvic acid solution. TOillustrate how this is done in the quasiparticle model, consider the complexation of Cu2+ by the unidentate ligands of fulvic acid in a background medium of KC104. A given class of these ligands can complex either one Cu2+,one K+, or one H+. The relative probability, P, that Cu2+ is complexed is given by the Gibbs factor (19):
where Qc. is a partition function for the bound copper ion; pcUis its chemical potential; k is the Boltzmann constant; and T is the absolute temperature. The relative probability that any cation is complexed, 6, is equal to a sum of probabilities like that in Equation 3: t(T3C(K,@H+CU) = QK exp(pK/kBT) + QH exp(PH/kBT) Qcu exP(,w./bT) (4) The mole fraction of Cu2+ on the site, xcu, may be calculated and expressed as a function of the activities of Cu2+, H+, and K+ in aqueous so-
in the general form: FIGURE 1
Pmton titration curve. for R l a b sludge fuMc acid 1.O g fuhrlc acldL, 25 "C,I = 0.1 M 2.0
where n p and CKpmay refer either to unidentate or bidentate ligands. Equation 1 I is exactly analogous to Equation 1. As indicated by Equation 9, the parameter CKp in general will depend on the temperature, the pressure, the ionic strength, the concentration of background electrolyte, and the pH value. The parameter ne can depend on all of these variables plus the total concentration of fulvic acid.
I
Analyzing experimental data The simple form of Equation I 1 lends itself very well to the analysis of experimental data on n M as a function of [M2+]by means of the conventional Scatchard plot method (19,23,24).In Figure 2 , a Scatchard plot for the complexes of Rialto sewage sludge fulvic acid with Cu2+ in a background of 0.1 M KC104 at pH 5.0 is shown in the upper curve. In this case, Equation I 1 could be applied in the form:
n l e K ~ [ C u 2 + I+ n c u = 1 +CKI[CU2+]
The curvature of the Scatchard plot .shows that more than one class of complexes has formed (24).That there are not, however, more than two classes is confirmed by the Scatchard plot of the parameter ncul,
0 11
8
10
7
5
-log H concentration
lution with help of the following equations ( 1 9 ) :
p~ = PA'
+ kT In
(6) where X = exp(p/kT); PA'' is the chemical potential of a cation A in aqueous solution in the standard state; and a A is the activity of a cation A in aqueous solution. The result of applying Equations 5 and 6 to Equation 4 is the expression: xc"(l)
constant and KcUKis a complex stability constant for Cu2+ complexation, relative to K+ exchange. The definition:
aA
(10)
=
KCuKaCu/aK 1 + (KHKaH/aK) + KCuKaCu/aK)
(7) where KAB 5
(QA/QEJ exP[(PA' - ps')/kTI
where yc. is a single-ion activity coefficient for Cuz+, permits Equation I to be rewritten as the expression:
(8) is a thermodynamic equilibrium constant for the exchange of cation A for cation B on the complexing functional group. K H is,~therefore, a protonation
The parameter cKc,(l) in this equation is a conditional stability constant for a Cu2+ complex with a unidentate ligand in a KC104 background. for a single The calculation of class of bidentate ligands proceeds very similarly to the calculation of xcu(l) and produces an expression of the same mathematical form as Equation IO, but with a different definition for CKcu(Z)from what was given for cKc,(l) in Equation 9 (19).This result implies that Equation 2 can be written
which is the lower curve in Figure 2. The straight line which results indicates that only a single class of complexes remains after the contribution of the first class has been subtracted from the measured values of ncu (19, 24). Figure 3 shows a plot of the data on nc. as a function of [Cuz+] that were used in the Scatchard plot analysis of Equation 12. The line through the data points is a graph of Equation 12 using the parameters: nl = 0.104 mol Cu/ mol fulvic acid; log % I = 3.85; nz = 0.803 mol Cu/mol fulvic acid; and log ' K 2 = 2.09. It is apparent that the quasiparticle model, as represented by Equation 12, can describe the measured values of nc. quite well. However, it should be emphasized that the model distinguishes different trace metal-fulvic acid complexes according to their apVolume 15, Number 4, April 1981
39s
gle-ion activity coefficients. The features that tend to distinguish one computer model from another, then, are the method of iterating the algebraic equations, the quantity and quality of the thermodynamic data stored, and the types of activity coefficient expressions utilized ( 2 6 . 2 7 ) . The mixture models of treated municipal sewage are especially welladapted to incorporation into computer programs because, by definition, they comprise a set of well-defined compounds whose reactions with cations have been characterized extensively in terms of thermodynamic equilibrium constants. Compilations of these equilibrium constants, prepared after a critical scrutiny of the analytical literature, are widely available (28, 2 9 ) . With this kind of consensus data base established, the application of a mixture model to predict equilibrium trace metal behavior in a natural water contaminated by treated municipal sewage has no unique features. The quality of the prediction will depend almost entirely on how well the model itself simulates the functional group chemistry in sewage, and not on the way it is interfaced with a computer program. Table 3 illustrates two examples of the use of the MS mixture model to predict the speciation of four important trace metals in natural waters at 25 "C. In each example, the model was introduced into the computer program GEOCHEM (30) simply by making a ratio between the measured organic carbon concentration (in g/m3) and 226 g/m3, which is the total organic carbon concentration of sewage sludge fulvic acid that corresponds to the
:IGURE 2
Scatchard lots 0.5 k4/& &It0 fuhric acid DH= 4.99 0.04
*
0
0.1
0.2
0.4
0.3
0.5
ncu or ncu' parent conditional stability constants and not according to their stoichiometries or molecular configurations. A single conditional stability constant, such as CK2, characterizes a set of complexes which may still include different ligands exhibiting a range of stoichiometries in their reactions with trace metals. The model by itself gives no information on the molecular structures of the complexes formed since it involves only macroscopic parameters. It may be noted in passing that the application of the model requires measurements of nM at fixed temperature, pH value, ionic strength, and total fulvic acid concentration. The anion of the background electrolyte must be Clod-, since the use of NO3or C1- ionic media will lead to trace metal complexes of the form MN03+ or MCI+, which then can compete with Mz+ for the fulvic acid ligands and produce spurious values of nM (25).
tion of a system of algebraic equations generated by the combination of mole balance with conditional stability, redox, and formation constants. The conditional constants usually are estimated by adjusting thermodynamic equilibrium constants, stored in a data file, with chosen expressions for sinFIGURE 3
Potentlometric titr8tion. of 0 5 kgl& Rialto sludge fuivic acid pH = 4.99 -C 0.04
0.5 0.4 3
2
02 01
Computer models
A variety of computer programs has been developed to predict the equilibrium properties of natural water systems ( 2 6 ) . Most general-purpose programs involve the numerical solu400 Environmental Science 8 Technology
03
c-
0.0 -+.a
J
-4.0
t
-3 5 log [Cu"]
*Tllra"l WBS 0
ow C"(ClOd)*
-30
,
-25
([CU*+]in mol/dm3)
-20
concentrations listed in Table I . The molar concentration of any one of the nine acids in the model, then, is equal to the product of this ratio and the molar concentration of the acid in Table I. This information about the model is all that is needed to do a numerical calculation with the computer program. No solid ohases are oermitted to form in the calculations summarized in Table 3. The soil water in Table 3 is the aqueous phase of a Delhi sand (Typic Xeropsamment), which was mixed with 2.25 g Rialto sewage sludge per kg soil, and incubated for one year in the laboratory at 25 OC. The water content of the soil was held constant at the percentage under onethird bar of pressure. The extracted aqueous phase was analyzed for Na, Mg, Si, K, Ca, Ni, Cu, Zn, Cd, Pb, organic C, co3, Po4, so4. and CI. With these data and the measured pH value, the computer calculation was performed. In all, 306 soluble complexes were considered during the calculation. The analytical data for the seawater in Table 3 were published by Nordstrom et al. (26). To these data, an organic carbon concentration of 260 g/m3 (2.16 X IO-' M ) was added to approximate the contamination of seawater by sewage sludge before dilution has taken place. The total molar concentrations of the nine organic acids in the MS model then were calculated and put into the computer program, along with the analytical data on the inorganic components. The total molar concentrations of Ni, Cu, Zn, and Cd input were not those given by Nordstrom et al., but instead were much larger values representative of water extracts of the sewage sludge. The computer calculation assumed oxic conditions and took into account the formation of 562 soluble complexes.
natural waters contaminated by
NiM) . .
4.59
Ni2+186.2),
[email protected])
4.66
WOH),(52.4), Or@. (26.1), CO3(12.5), NP'(5.5)
4.54
Cu2+(43.7).Org. (43.6). - S0.(5.1)
4.96
Org. (72.5). B(0H)c (26.8)
4.33
WOlih(62.73, Znzf(16.6). C047.7).
3.28 Zn2+(85.5), SO.(lO.O)
V..,..,
5.30 Cd2+(72.1), C1(14.4), SOd10.8)
concentration. It should be noted that previous computer calculations of trace metal speciation in oxic seawater (26, 31) have not included borate complexes ( 3 2 ) , and therefore have often indicated that carbonate or hydroxide complexes of Ni, C u , and Zn would predominate. Although the published stability constants for the borate complexes are certainly not definitive ( 3 2 ) , the contrast between previous speciation calculations and the model results in Table 3 underscores the importance of completeness in the thermodynamic data base for the chemical modeling of natural waters. The relatively small competitive effect of the sewage sludge organic fraction on trace metal speciation indicated in Table 3 evidently can be understood on the basis of the selectivity rule (7),which states that the extent of complex formation between a metal and a ligand is proportional to the product KCT, where K is the stability constant of the complex and CT is the total molar concentration of the Competition with ligands metal. This product, applied to the The most striking characteristic of organic ligands, often is much larger the model results in Table 3 is the in- for Group IIA cations than for trace ability of the sewage organic fraction metal cations. That is because CT is to compete effectively with other li- usually three or more orders of maggands for the trace metal cations, ex- nitude larger for the former, whereas cept in the case of copper. In the soil K, except for copper, is approximately water, the dominant species is always the same in the MS model for either the (potentially most toxic) free metal set of metals. The net result is that the cation, whereas it is either a borate or organic ligands tend to be complexed a chloride complex in the seawater. For with calcium and magnesium. In the copper, organic complexes amount to seawater calculation, the additional 44% of the soluble metal concentration factors of a total borate concentration in the soil water and 73% of the soluble equal to that of the organic ligands and metal concentration in the seawater. a positive difference of about four orFor the other metals, organic com- ders of magnitude between K for boplexes were less than 5% of the total rate complexes with the trace metals
uersus the Group IIA metals combine to give the borate complexes a decided competitive advantage over organic complexes of the trace metals.
Fulvic acid difficulties The incorporation of the mean fulvic acid unit model into a computer program is not straightforward because the model parameters are measured values of conditional stability constants for a heterogeneous mixture instead of thermodynamic stability constants for well-defined organic acids. The situation is made more complicated by the fact that, a t present, the conditional stability constants can be determined only potentiometrically. Standard spectrophotometric methods cannot be used because they give spurious results for mixtures of organic ligands (33). Polarographic techniques also are not applicable because they require variation of the total organic ligand concentration, which, however, must be held constant when the trace metal complexes of sewage sludge are investigated (19.34). The values of the common logarithms of < K I and W 2 in Equation 12 that have been determined potentiometrically for complexes of Ca2+, Cu2+, Cd2+, and Pb2+ with Rialto sewage sludge fulvic acid (35) are listed in Table 4. The relatively low values of log c K ~and log eK2 are not unexpected in a heterogeneousmixture such as sludge fulvic acid, where the molecular configurationsof the ligands will be highly variable. They will provide for a continuum of environments, instead of a discrete set with well-differentiated affinities for metal cations, as would occur for a single organic acid. Volume 15, Number 4, April 1981
401
logCK~=0.06716+7.1488Y ( r 2 = 0.989) (14b)
of log cK,and log OK2 in Equation 12 for nine ent metal cations (parentheses denote measured
&I2+
Ca2+ Mn2+
Fe2+ Ni2+ cu2+
Zn2+
w Clr,
4=IC*
Y("m)
2.71 (3.12) 3.93 3.96 3.81 (3.66) 3.54
0.69 1.23 2.23 2.26 2.08 (2.11) 1.74 (2.27) (2.62)
0.067
CdZ+
w*+ bst
High affinities of organic ligands for chemically significant parameters can .metal cations generally develoD from be found that characterize a class of favorable relazonships betwee'n both complexes of interest and that permit the spatial orientation and the enera linear relationship to be established getics of the bonding orbitals in metal between a suitable function of the paand ligand. This kind of synergism is rameters and the common logarithms not probable for a metal cation interof the stability constants of the comacting with a multiplicity of highly plexes. variable and competitive ligand conIn the case of the trace metal-sludge figurations whose resultant effect is fulvic acid complexes, one significant likely to be produced by comproparameter appears to be the Misono mise. softness parameter (37), which is a Table 4 also lists values of log C K ~ quantitative measure of the Lewis acid and log EK2 estimated for five addisoftness of a metal cation. The retional bivalent metal cations according gression equations: to the methods of linear free-energy l0gCKi = 2.214 5.6585Y relations (36). The basic premise of this approach is that a small set of ( r 2= 0.998) (14a)
+
are used to calculate the estimated stability constants in Table 4. Here, Y is the Misono softness parameter (in nm) and the numerical values are the result of a linear regression of the measured values of log e K ~or log cK2 .in Table 4 on Y , with r 2 being the correlation coefficient. The measured ~ the CdZ+complex value of log E K for was not employed to obtain Equation 14a because it is believed that this complex involves only electrostatic bonds and, therefore, is not dependent on the Lewis acid softness of Cdz+. and log E K ~ The estimated log values can be of value in applying the mean fulvic acid model until more reliable, experimentally determined, conditional stability constants are available. Speciation in soil water
Since the conditional stability constants in Table 4 refer to an aqueous solution of 0.1 M ionic strength a t pH 5.0, they should be used only to model trace metal behavior in natural waters near that ionic strength and pH value. Table 5 illustrates the percentage speciation of Ni, Cu, Zn, and Cd calculated according to the mean fulvic acid model for the aqueous phases of three soils that meet this criterion. For these calculations, performed by the GEOCHEM program, the mean fulyic acid unit was treated as a mixture of two complexing ligands. The molar
TABLE 5
Mean fulvic acid model predictions of trace metal speciation in three soil solutions contaminated by municipal sewage sludge
Zn(ll)
Cd(ll)
4.67
Ni2+(67.6),Org. (13.6). Sod 10.0), C03(5.1)
5.17
Ni2+(65.6),0rg. (20.7), S04(10.4)
6.07
Ni2+(73.0), Org. (12.9). SO,( 10.7)
5.46
C0~(44.6),Cu2+(37.6), Org. (7.9). SO4(7.O)
5.60
Cu2+(53.5), Org. (17.9), COS(15.9), Sod( 10.7)
5.90
Cu2+(59.6), COdl6.1), org. (11.2), SOa(l1.0)
4.62
2n2+(72.0). SOd13.4). Org. (7.6)
4 6
Zn2+(71.0), S04(14.2), Org. (11.9)
4.70
Zn2+(75.9). SOa(14.0) Org. (7.1)
4.06
Cd2+(52.3), Org. (20.9). SO4(13.4), Cl(12.1)
4.48
Cd2+(63.5). SO4(14.9] Org. (14.0). Ci(5.7)
36 Cd2+(53.0), Cl(17.3). Org. (14.1). SOd12.6)
tyP * Typic Xerament. pH 5.7. Cwnputed ionic 8t-enam = 0.11 M. Orgsnic C = 286 g/m3. Micstedby tW. AbNptic Durixeralt. pH = 4.8. caputed ionic Saen@h = 0.07 M. -IC ionlc slr= 0.06 M. Organic C = 177 g/ma.
'
402
Environmental Science a Technology
Metal w i e s tollowed by percentageat G. Canptsx< C = 357 g d . aTypic NaWxeraH. pH = 5.2.
concentration of each ligand was calculated with the expression (38): Org’ FUTi
X
=226
2.06 X IO-) 1.21 ( i = 1, 2) (15)
calibration of mixture models. For selected sewage-natural water systhe soluble Ira= predicted from a quasiparticle model can be compared with that predicted from a mixture model and adjustments can be made in the latter when discrepancies appear. Perhaps this approach is the best means of utilizing quasiparticle models, because Of their basis in data but limited domain ofapplicabi~ity,
(18) Sposilo. G.: Holtzclaw, K. M.: Keech. D. A.SoilSCi. Sm. Am. J . 1977,4l. 1119. (19) Sposilo. G.: Holtzclaw. K. M.: LeVesque-Madore.C. S. SoilSci. Sw. Am. J . 1979, 43. I 148. (20) Sposito.G.: Holtzclaw. K. M.: Baham.J. soil Sei. Sac. Am. J . 1976,40.691. (21) Sporito.C.:Schaumberg,C.D.:Perkins. T.G.: Haltzclaw. K. M. Enuiron.Sn‘. Techno/. 1978,12,931. (22) Hill, T. L. “An Introduction to Statistical
Here*“Org. c” is the measured Organic carbon concentration in g/m3; ni Thermodynamics”:Addison-Wesley: Readis the capacity parameter appearing in ing, Mass., 1960. (23) Scatchard. C. Ann. N.Y. Acod. Sri. 1949, Equation 12; and the last factor is the 51.660. molar concentration of fulvic acid that (24) Scatchard.G.:Coleman.J.S.;Shen,A. L. corresponds to 226 g C / d . The factor 1. Am. Chem. Sor. 1951.79. 12. 1.21 in Equation IS is the average (25) Sposito, C.: Holtzclaw. K. M. Soil Sei. Gratitude is expressed to Kenneth M. Soc. Am. J. 1979.U.47. valueof(n, + n 2 ) for thecomplexesof and Cynthia S. LeVesque(26) Nordstrom. D. K.. et al. Am. Chem. Sm. fulvic acid with Ca2+3CU2+*Cd2+,andHoltzclaw Symp. Ser. 1919.93.857. Madore for their technical assistance and PbZ+.The average vahes Of nl and nz (27) Leggett, D. J. Talanra 1977.21.535. ideas. The author has gained significantly were 0.1 1 and I . I , respectively. The i n his understanding of the chemistry of (28) Martell. A. E.: Smith, R. M. “Critical Stability Constants”: Plenum Press: New natural waters through the constant encomputer calculation took into account the formation of212solublecomplexes couragement and support of Albert L. 1974-76. (29) Perrin. D. D. “Stability Constants of among the IO metals and seven ligands page. former director of K~~~~~~ F ~ ~ ~ of Soil Science at the University of whose total molar concentrations in dation ~ x ~ California, 1979. the ’Oil solutions were determined exNote: This article was read and com(30) Spmita.G.: Mattigod,S. V.“CEOCHEM: perimentally. mented on by Dr. L. E.Sommersof Purdue A Computer Program for the Calculation of A Of the results in Table University (West Lafayette, Ind.). Chemical Equilibria in Soil Solutions and indicates that the mean fulvic acid unit Other Natural Water Svrterns”: _............... , ~ Keirnev Foundatiohz Soii-Science; University df model. like the MS mixture model, References California: Riverside. Calif.. 1980. suggests that soluble trace metal(31) Dyrrsen. D.: Wedbarg. M. In “The Sea. sewage complexes will not be domi- ( I ) “ProceedingsofaWorkshopon Asrimila. ‘01.5. MarineChcmistry”:Goldberg. E. D., tive Capacity of U.S. Coastal Waters for nant species, The principal qualitative New York. 1974. pollutants-: Goldberg.E. D., Ed.: U.S. D ~ ~ Ed.: ~ Wiley-lnterscience: . R: L. Gemhim. Cosmorhim.Acta difference between Table 3 and Table ,,fcommercc: Washinpton, - D,c,.gold be^ (32!Eaylt,~ IYIIU,44. l l S l 5 is the more widespread Occurrence of 1979. (33) Crosser. M. L.: Allen. H. E. Soil Sci.. (2) Reutcr. J. H.; Perdue, E. M. Gemhim. organic complexes predicted by the 1911. 12J. 268. Acta 1971.41. 325. mean fulvic acid unit model. This at- (3)Cosmochim. (34) Sposito. C.: Haltzclaw. K. M.: LeVesPage, A. L.“Fateand Effects afTrace Eltribute of the model derives from the que-Madore.C.S.SoilSci.Sor. Am. J. 19‘18. ements in Sewage Sludge When Applied to 42.600. relatively close clustering of log K Agricultural Lands.’’ Report No. EPA(35) Spmito. G.: Holtzclaw. K. M.: LeVes67012-74.005: U.S. EPA Cincinnati. Ohio. values in Table 4. The values of cKi que-Madore.C. S. Soil Sei. Sm.Am. J. (in 1974. ( i = I , 2) for the two organic ligands press). (4) (a) Morel. F.M.M.: Schiff. S. L. “Geodo not differ too much among the four (36) Sposito. G. “The Thermodynamics ofSoil chemistry of Municipal Waste in Coastal Solutions”: Oxford Univ. P m : Oxford. U.K. trace metal cations; therefore, selecWaters.” Report No. 259: Parsons Labara(in press). tory, MIT Cambridge. Mass.. 1980. tivity more or less follows the relative (37) Huheey, J. E. “Inorganic Chemistry”: (b) “Modeling Wastewater Renovation Land order of CTvalues in Table 5. On the Harper and Row: New York. 1978. Treatment”: Iskandcr. 1. K.. Ed.: John Wiley: other hand, in the mixture model, a (38) Sposito. C.: Bingham. F. T.; Vadav. S. S.: NewYork. 1981. Inouye. C. A. Soil Sci. Sac. Am. J. (in rewider range of values for K exists and tSI M In“Fatenf ~ .............. , o d F~M M~:Ymstd~.ILG ...... view’. Pollutants in the Air and Water Environselectivity-is much less directly related mcnts”: Suffet. I. H.. Ed.; John Wiley: New to CT for the trace metals. “^_I.
,“,$?~;~p~~~”’~~fir~~l
,.,?7 I”IL.171,.
Predictive value
To the extent that the complexation reactions of trace metals determine their potential to cause toxicity effects in treated sewage-natural water mixtures, the use of simplified models to describe the functional group chemistry of the soluble organic fraction of sewage will be of predictive value. Of the two available classes of functional group models, the mixture models possess a greater breadth of application to natural waters and greater ease of interfacing with chemical equilibrium computer programs. Since these models are difficult to validate directly, their predictions are the basis for the evaluation of their soundness. In this respect, the other class of models. exemplified by the mean fulvic acid unit model, can be of use in the
(6) Schaumberg. G. D.; LeVesque-Madore. C. S.:Swsito.C.:Lund.L. J. J. Enuiron.0~01. 1980, 9.291. (7) FraustodaSilva, J. J. R.; Wil1iams.R. J. P. Strurt. Bonding 1916,29,67. (8) Neibar. E.: Richardson. D. H. S. Enuiron. Pollut. 1980, IS. 3. (9) F1arence.T. M. WorerRes. 19l7,11,68l,
-
and references cited therein. (IO) Allen. H. E.: Hall, R. H.: Brisbin. T. D. Enuiron. Sei. Techno/. 1980, 14. 441. and referencescited therein. ( 1 1 ) Ahrland. S. Struer. Bonding 1913, 15. 167
(lij.Morel. F. M. M.; Wstall.J. C.;O’Melia. C. R.: Morgan. J. J. Emiron. Sci. Techno/.
~..
19’15.9.156. (13) Mattigod. S. V.; Sposito C . Am. Chrm. Sm. Symp. Sw. 1979.93.837, (14) Schnitzer. M.; Khan.S. U.“SoilOrganic Matter”: Elxvier: Amsterdam, 1978. (15) MacCarthy. P.:Smith.G.C. Am. Chem. Sm. Svmn. Ser. 1919.93~201 ~~
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(17) Lundqvist, S. I n ‘ ‘heorv ‘ 1 ~ of ~....~Condensed ...~ .... ~...
Matter”: Salam. A.. Ed.: lnt. Atomic Energy Agency: Vienna. 1968.
Garrison Sposito is professor in the Department o/Soil and Environmental Sciences at the University of California, Riverside. His research interests include the physical chemistry of natural water systems and the statistical mechanical theory oftransport processes. H e is the author of textbooks on quantum mechanics and classical dynamics and o a monograph, “The Thermodynamicso/oilSolutions.” to be published this year by the Oxford University Press. Volume 15, Number 4, April 1981 403
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