Environ. Sci. Technol. 1985, 19, 544-551
University of Missouri Press: Rolla, 1976; Vol. 10. Stumm, W.; Morgan, J. J. "Aquatic Chemistry", 2nd ed.; Wiley-Interscience: New York, 1981; pp 1-780. Cufrin, B. L.; Moffat-Kennedy,R.; Clark, A. N.; Wilson, D. J. Sep. Sei. Technol. 1979,14,669-687. Clarke, A. N.; Wilson, D.J.; Clarke, J. H. Sep. Sei. Technol. 1978,13,573-586.
Iwasaki, I.; Cooke, S. R. B.; Colombo, A. F. U.S. Bureau of Mines, Avondale, 1960, Report RI 5593. Parks, G. A. Adv. Chem. Ser. 1967, No. 67, 121-160.
(30) Parks, G . A. Chem. Rev. 1965, 65, 177-198.
Received for review September 24, 1984. Accepted December 26,1984. This research was sponsQred in part through a project supported by the Hawaii Natural Energy Institute through Department of Energy Contract DE-FG03-81ER10250M003. The Zeta meter used in these studies was provided by Ed Laws through Solar Energy Research Institute Subcontract X E 09013-01. This is Hawaii Institute of Geophysics Contribution No. 1586.
Using Electrophoresis in Modeling Sulfate, Selenite, and Phosphate Adsorption onto Goethite Douglas D. Hansmann* and Marc A. Anderson Water Chemlstry
Program, University of
Wisconsin, Madison, Wisconsin 53706
We evaluate methods for determining two quantities generally considered necessary in modeling adsorption. First, the electrical component of net binding constants is determined by electrophoresis in conjunction with pH measurement. Second, three techniques for determining the maximum concentration of available surface sites are compared. We use a Stern model to make out evaluations; however, the results should be applicable to adsorption modeling in general. Electrophoretic mobility data are modeled quite successfully, but the empirically determined maximum surface-site concentration on colloidal goethite (a-FeOOH) varies considerably for sulfate, selenite, and phosphate despite their similar sizes and binding mechanisms. We suggest that aggregation processes, due to both proximity to the isoelectric point of the solid and adsorbate bridging between particles, may have significant effects on surface-site availability.
Introduction Suspended particles can play a major role in the attenuation and transport of otherwise-dissolved compounds because of combined chemical and electrical interactions resulting in adsorption. The practical value of correlating the extent of adsorption with changes in either particulate or solution character is well recognized and continues to prompt considerable research. Natural adsorption processes generally occur with a number of distinct adsorbate species and particulate surfaces present. However, current models for predicting the extent of adsorption in relatively simple systems, containing only one or two adsorbates and a single adsorbent, have not always been successful and are often cumbersome in practice. We evaluate some of the methods for determining adsorption model parameters in an attempt to refine our predictive capabilities. In general, existing models for predicting the extent of adsorption can be divided into two schools of thought. First, there are surface complexation models based on plausible surface reactions between adsorbate molecules and particle-surface sites (1-6). These models have the following form:
A + =SL& =SA+L (1) where A is a dissolved adsorbate molecule near the particle surface, =SL is a surface site with an attached leaving group, =SA is a surface site with an attached adsorbate molecule, and L is a dissolved leaving-group molecule near the particle surface (in an aqueous solution with only one 544
Environ. Sci. Technol., Vol. 19, No. 6, 1985
adsorbate species A considered, L must be H+, OH-, or a water molecule). Adsorption density is predicted from a simultaneous solution of the equilibrium expression(s) associated with eq 1,an adsorbate mass balance (eq 2), and a surface-site mass balance (eq 3). (2) [A] + N(=SA)= [A],,1 [A] is the dissolved adsorbate concentration (pM), N is the adsorbent concentration (g/L), (=SA) is the adsorbate density on the particle surface (pmol/g), and [AIbd is the total analytical adsorbate concentration (pM). (3) (=SL) (=SA] = (S3)btd (S3L)is the density of unfilled adsorbent sites (pmol/g) and (=Sjtotal is the maximum concentration of available adsorption sites (pmol/g). Since complexation models are, in theory, based on accurate molecular descriptions of actual reactions, available spectroscopic evidence should confirm surface species predicted by the proposed set of reactions and associated equilibrium constants (Kc). In the case of phosphate adsorption onto goethite (a-FeOOH), infrared spectroscopic studies indicate a binuclear coordination of phosphate ions to two iron atoms on the particle surface (7). However, a complexation model allowing either mononuclear or binuclear coordination among its set of proposed reactions (5) predicts mostly mononuclear species over a wide range of pH and total phosphate concentration. Experimental data are successfully modeled in spite of this discrepancy by using empirically determined equilibrium constants. Alternatively, there are statistical models where the ratio of adsorbate-occupied to adsorbate-free surface sites is related to the mole fraction of adsorbate remaining in solution (8-13). (=SA)/(=SLJ= K,X (4)
+
Here, a partition coefficient, K,, is empirically determined for each type of surface site, and eq 2-4 are solved simultaneously to predict adsorption density. In contrast to the surface complexation approach, this model is not constrained by an a priori knowledge of binding mechanisms or reaction stoichiometry. Both equilibrium constant (eq 1)and partition coefficient (eq 4) are commonly expressed in terms of the Gibbs free energy: K,,, = e-AGmt/(RT) (5) where AG,, is the total observed free energy change due to adsorption, R T is the gas law constant times the kelvin
0013-938X/85/0919-0544$0 1.50/0
0 1985 American Chemical Society
temperature, and Knetis the net equilibrium constant or partition coefficient. Since work is involved in bringing charged adsorbate molecules through the electric field produced by a charged particle, the net energy of adsorption is often divided into intrinsic and electrostatic components. AGnet
=
AGintrinsic
+ AGeletrostatic
(6)
For a given experimental system, both statistical and surface complexation models of adsorption describe the same physicochemical process and should have some features in common. Certainly, both electrostatic energy w d concentration of available adsorption sites ((=Slbtdin eq 3) should be model independent. In the present work, we compare the adsorption of three anions having wideranging affinities for colloidal goethite. Quantification of AGeleCtrostatic and (=S)b,l is investigated by using classical Stern theory as the framework for a statistical model. In the course of our study we do not mean to suggest that the Stern model is superior to the other available models of adsorption referenced above. However, we feel our results do have implications for adsorption modeling in general.
Theory The Stern model of adsorption (9) considers both the fraction of surface sites occupied by adsorbate ions and the adsorbate mole fraction in solution. These quantities are related by a Boltzmann distribution based on the difference in energy between dissolved and adsorbed states (14). Mathematically, this model can be expressed by combining eq 3-6 and rearranging:
Site Density. An empirical determination of (=SIbM can be made by adding a known excess concentration of adsorbate, measuring the remaining dissolved concentration after equilibration with particulate material, and attributing the amount removed to a saturation of available surface sites. This presupposes that there are no competing reactions such as surface precipitation or adsorbate complexation in solution. Our research on goethite indicates that this empirical value is not always consistent with results from alternative methods for site density determination such as the two techniques described below. (1)Infrared spectroscopic studies suggest that oxyanion surface complexation occurs by displacement of singly coordinated surface hydroxyl groups (15). There is one singly coordinated hydroxyl per unit cell on each of the two predominant goethite crystal faces (16, 17), and unit cell dimensions for each face are well-known (18). Goethite crystal dimensions determined by transmission electron microscopy are used to assign an appropriate fraction of the total N2 BET surface area attributable to each crystal face, and site density in either moles per mass or moles per surface area can then be calculated. (2) The second method assumes that an equal number of sites is available for both surface protolysis and oxyanion adsorption (5). Therefore, results from acid-base titration of the surface should simultaneotlsly provide concentration of available oxyanion adsorption sites and the protolyzable site density. However, recent research indicates that cations and anions may bind a t different locations (19)) so the site density for each type of ion may not be the same. Electrostatic Energy. Modelers continue to debate how to formulate the electrostatic component of adsorption energy (20). Ion partitioning between particle surfaces and
bulk solution is influenced by charges on both ions and particles, and electrostatic energy can be evaluated by measuring the work required to bring ions from bulk solution to the surface binding plane. Since voltage is defined work per unit charge, the product of binding-plane potential (ICbp) relative to bulk solution and the charge ( 2 0 associated with 1mol of ions yields a measure of electrostatic energy. AGelectrostatic
= zFhp
(8)
Although there is no method for measuring this bindingplane potential directly, electrophoretic mobility can be used to determine potential at the plane of shear, and this in turn can be related to potential at the binding plane. Electrophoresis refers to particle movement through a fluid caused by an electromotive force. In addition to this electric field, the particle is affected by Stokes' friction acting in opposition to the field, which is a function of particle size and viscosity of the medium. Calculation of shear-plane, or {, potential from electrophoretic mobility was first derived by von Helmholtz (21) and von Smoluchowski (22): { = Uv/(tot) = (14.1)U (at 20 "C in water) (9) where U is electrophoretic mobility [pmcm/(V.s)], eo is F/m), E is the the permittivity of free space (8.854 X solution dielectric constant, q is viscosity (poise), and t is f potential (mV). Later work (23, 24) showed that this relationship was valid only for values of Kr > 100 where r is the particle radius and K is the reciprocal Debye length. For Kr < 0.1, this research resulted in a second limiting relationship, the Huckel equation. { = 3U7/(2toe) = (21.2)U (at 20 "C in water) (10) Between these two limits, additional forces become significant. Just as the particle-surface charge is attraeted to one of the poles in the applied direct current field, counterions in the particle atmosphere are repelled by this pole, resulting in the relaxation effect whereby the center of the ionic atmosphere lags behind the particle center itself. Also, ions in the particle atmosphere can experience viscous drag with respect to surrounding solvent molecules. Both effects are accounted for in the theory of Wiersema et al. (25) for spherical particles, and their results have been extended to cylindrical particles by Stigter (26,27). The relationship between mobility and {potential has been experimentally verified by Ottewill and Shaw (28). Once { potential has been determined, the relationship between this quantity and binding-plane potential must be established. The binding plane must be located at or inside the plane of shear, since ions cannot be considered bound to the surface unless they move with the particle. Consequently, I&pl I In, any difference being due to electrostatic decay across the intervening distance. If the shear plane is placed at the outer edge of the specifically adsorbed layer (89-31),coincident with the beginning of the diffuse layer (i.e., { = ICdiffuse), we can use a capacitor model of the double layer which assumes a linear potential decay between binding and shear planes. Charge outside the shear plane can be obtained by using Gouy-Chapman theory (31): at = -11.74fi
sinh [zF{/(2RT)]
(11)
ag is diffuse layer charge (pC/cm2), C is total electrolyte concentration in equivalents/liter, and t is {potential in volts. By use of a value of 20 pF/cm2 for outer-cornpact-layer capacitance (29,32), binding plane potential can be calculated. Environ. Sci. Technol., Vol. 19, No. 6, 1985
545
$bp
= s" - g[/20
Sulfate
(12)
This result is used directly in solving eq 8 and is also necessary for ion charge ( 2 ) determination in that equation. The average charge on a protolyzable ion in solution is a pH-dependent number and can be calculated by using acid dissociation constants and solution pH. However, pH at the plane of binding is affected by the particle's electric field and, therefore, should be corrected as follows for calculating z (12):
= x .-c n 1-
I"
-
1.OC
.o
-
--
- 2.0 - 3.0
-
(H+)bp= (H+)bup&-F~bp/(RT) (13) where (H+)bp is hydrogen ion activity at the binding plane. Intrinsic Energy. With the theory developed above, it is now possible to rewrite eq 7 solving for intrinsic free energy of adsorption in terms of measurable quantities.
(14) For a given adsorbate-adsorbent pair, this intrinsic energy should be invariant as a function of pH or reactant concentrations. We use this premise to test our ability to determine (=S)total and $bp.
Materials and Methods All experiments involved batch equilibration of radiolabeled adsorbates with dilute goethite slurries. The phosphate data are from Stanforth (33) in which the equilibration time was 4 h at a goethite concentration of 74 mg/L and 0.002 M ionic strength. Other than these exceptions all experimental conditions were as follows. Goethite (a-FeOOH) was prepared according to Atkinson et al. (34) by Stanforth (33). Transmission electron microscopy revealed acicular particle monomers, about 35 nm X 25 nm X 300 nm in size. Using a 430X magnification light-field microscope, aggregates were also seen to be elongated, approximately 0.2 pm in cross section. The extremes in particle size result in a range of Kr values from 1.8 to 10 at lo-, M ionic strength. N2 BET surface area was 33 m2/g, and X-ray diffraction patterns confirmed the absence of noticeable hematite or amorphous Fe(OH), contamination (35). Preequilibration was accomplished by filling 100-mL polyethylene bottles with a solution containing the adsorbate of interest (ranging between 2 x lo4 and 2 x M) and either HNO, or NaOH to achieve the desired pH (generally between 4 and 10). A rqdioactive label was included (32P,75Se,or 35S), and the ionic strength was adjusted to lo-, M with NaN03. Bottles were kept at 20 "C for 24 h in a New Brunswick shaker, rotating at 160 rpm. Other stock containers and pipets were also filled with preequilibration solutions. Pretreated bottles were emptied, refilled with fresh solution, and equilibrated for l h in the constant-temperature shaker. Next, 0.5 mL of 6.0 g/L stock goethite suspension was added (the final goethite concentration was -30 mg/L), and bottles were immediately returned to the shaker. With these low solids concentrations we were able to achieve high levels of surface coverage with relatively low adsorbate concentrations, thereby minimizing competing reactions such as surface precipitation or solution complexation of the adsorbate. Also, particle collision frequency, and, hence, particle aggregation, was kept to a minimum at these solids concentrations. After a 24-h equilibration, pH was measured with an Orion 801 pH meter and a Corning combination electrode, and electrophoretic mobility was determined with a PenKem laser zee meter. (The mobility histogram and 546
Environ. Sci. Technol., Voi. 19, No. 6, 1985
,
:
I ' :
4.
~
I , : , I , : , I , : 5. 6. 7.
i
I ,
8.
I , :
~,
:
I . : :i
9 . 1 0 . 1 1 .
-1.0-
a) Selenite 2 . 0 ""Ol/L
- 3.0
Phosphate 2 . c UrnOl/L
+
-2.oc
5.c
drnOl/L
u\_
PH
Figure 1. Electrophoretic mobility is a function of both pH and adsorbate concentrationfor goethite in the presence of sulfate, selenite, and phosphate.
Brownian motion spectra shown in the last two figures were obtained on a PenKem system 3000 electrokinetics analyzer. Here, the goethite was obtained from a second preparation with an N2 BET surface area of 81 m2/g and monomeric crystals 80 nm in length.) In addition, two aliquots were filtered through a 0.4-pm Nuclepore filter supported by a polycarbonate apparatus. The first portion was wasted, and the second was used for dissolved adsorbate determination by radioactive counting techniques using a Packard Model 3320 liquid scintillation counter. Adsorption density was calculated from the difference between initial and dissolved concentrations and normalized with respect to solid mass. Adsorbate pK values were determined by acid-base titration for selenite, since literature values proved unreliable. Under our experimental conditions, pK1 = 2.5 and pK2 = 8.45.
Results and Discussion The electrophoretic mobility of colloidal goethite in the presence of adsorbed anions is a complicated function of both pH and adsorbate concentration (Figure 1). Given the particle size range and ionic strength of our goethite slurries, and assuming a cylindrical particle shape as a model for our acicular crystals and aggregates, the relationship between shear-plane potential and electrophoretic mobility falls between the two limiting conditions described by eq 9 and 10. By use of data from Stigter (26), Table I lists the appropriate constant to be used in place of "14.1" in eq 9 for a series of mobility ranges. The error terms listed in the table reflect the range in particle size. By use of eq 8-13 and Table I, the relationship between mobility and AGelectrostatic can be established (Figure 2), and it is apparent from Figures 1 and 2 that AGelectrostatichas a functional dependence on both pH and total adsorbate
S ULFATE
P H0S PHATE
SELENITE
3.
I
--
-3.0 -2.0 -1.0
+ ~~1 -1.
-1.
- 4.
- 4.
- 5.
- 5.
- 5.
Mobility
ii
Mobility
cm/v*al
Figure 2. Electrostatic component of the binding energy is related to electrophoretic mobility. FREE ENERGY OF SULFATE ADSORPTION
Table I. Constant To Be Used in Place of "14.1" in Equation 9 for a Series of Mobility Ranges" U , pm.cm/ (V-s)
constant
0.0-0.5 0.5-1.0 1.0-1.5 1.5-2.0 2.0-2.5
18.2 i 1.9 18.1 f 1.9 17.9 f 1.8 18.2 f 1.9 18.5 f 2.0
U , pm.cm/ (V-s) 2.5-3.0 3.0-3.5 3.5-4.0 4.0-4.5 4.5-5.0
{sSltatal = 140. umol/g
constant 5 . 0 umol/L 5.0 umol/L A 2 0 . 0 umol/L
18.9 i 2.2 19.5 i 2.1 20.4 i 2.1 22.3 i 2.1 24.4 i 1.8
+
Based on data from Stiater (26) for cylindrical particles.
concentration. For each of the three oxyanions of interest, the net energy of adsorption based on the Stern model (eq 6 and 7) is also a function of pH and adsorbate concentration (Figures 3a-5a). However, when AGelectrostaticis subtracted from these net energy values, the resultant intrinsic energy of adsorption does not show any clear dependence on either variable (Figures 3b-5b). It is apparent that the net energy of adsorption contains a potentially large but relatively constant intrinsic component and a smaller, but highly variable, electrostatic component. In the above analysis, a value for the maximum concentration of available adsorption sites has been assigned for each anion. For selenite and phosphate, these are empirical values of 80 and 43 hmol/g, respectively, based on surface saturation (Figure 6). For sulfate, no surface saturation was observed due to analytical difficulties in obtaining this value. Since +SA) is determined by the difference between [A],,, and [A] in eq 2, the precision of this determination becomes unacceptable as the difference becomes small (e.g., N(=SA) < O.O1[A],d) for weakly bound adsorbates such as sulfate. We describe two alternative indirect methods for site density determination under Theory. By the first technique, using crystal morphology characterization in conjunction with BET surface area measurements, we calculate a maximum site density of 140 pmol/g. With the second method (=SJtotal= 120 pmol/g by using titration results from Sigg and Stumm (5) and adjusting for the differences in BET surface area between their goethite and
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FREE ENERGY OF PHOSPHATE ADSORPTION ~
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9.5
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.
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8.
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'
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Figure 5. Net energy of phosphate adsorption (a) and the intrinsic component (b) are shown as functions of pH and total phosphate concentration.
of 140 pmol/g in Figure 3. However, this maximum should apply equally well to all three oxyanions in theory, since their binding mechanisms are thought to be similar and they are all approximately equal in size. We can illustrate value, as the effect of assuming the theoretical (=S]totel opposed to the empirical values used in Figures 4 and 5, for selenite and phosphate in the following manner. With the assumption that AGintrinsicis constant for a given adsorbate-adsorbent pair, eq 6 can be treated as a linear relationship between AGnet and AGelectroshtic where the slope should be equal to unity and the intercept is AGintrinsic.Figures 7 and 8 show this relationship, comparing the use of empirical vs. theoretical values for selenite and phosphate, respectively. The dashed lines depict a slope of 1 and an intercept of -AGintrinsic(determined by averaging the data in Figures 4b and 5b). The ability to fit data with this slope and intercept tests the adherence of the system to a Stern model of adsorption. In Figure 7 there is little or no qualitative improvement values for made by choosing either of the two (=Sjtotal selenite uptake. However, in both cases, noticeably lower -AGn& values are obtained near the isoelectric point (pHiep) where shear-plane potential, and hence AGelectrostatioapproach zero. We suggest that particle aggregation reduces the number of sites available for selenite adsorption near the pHiep,and our research is continuing in this area. Clearly, such a decrease in (=SItoawill increase values for -AGnet (see eq 6 and 7) and, therefore, will increase values near the pHie, in Figure 7. The empirical (=Sltodvalue for phosphate uptake yields a markedly better Stern model fit compared to the theoretical value, as shown in Figure 8, Also, in this system there is no apparent reduction in max.imum site density 548
Environ. Sci. Technol., Vol. 19, No. 6, 1985
ADSORPTION DENSITY AT THE ISOELECTRIC POINT
[pliep
(UM)
Figure 6. Adsorption density is shown as a function of adsorbate concentration remaining in solution. Each data point is obtained by extrapolation from results obtalned on both sMes of the isoelectric point (iep), based on electrophoresis measurements.
near the pHiep. Instead, the empirical (=S]toM value is considerably lower than the theoretical value throughout the range of pH and concentration studied. It has been suggested that phosphate can form bridges between goethite crystals (36),thereby greatly reducing the total number of available sites regardless of proximity to the PHiep. Our recent research supports this explanation. We have previously shown that particle mobility decreases with phosphate uptake (Figure 1). In addition, the mobility distribution about the mean value narrows considerably with adsorbed phosphate (Figure 9). With a strongly bound ion such as phosphate, a narrow distribution may
'
~
'
Selenite:
a)
i
m
i
11.5 12.0
+/
b)
11.5 11.0
+ AM /
ll.O 10.5
/
10.5
(~s}total =
10.0
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11
m+ L
.
X 15.0 pmol/L
r
6.5 --
LL .3.0
-2.0
- 1.0 .O 1.0 2.0 - AGslsctrostatic( k c a l / m o l )
3.0
Flgure 7. Relationship between net energy of selenlte adsorption and its electrostatic component is compared by using both empirical (a) and theoretical (b) values for the maximum concentration of avallable adsorption sites. The dashed lines depict a slope of 1 and an intercept of -AG,-
a)
12.0
m 11.5
-- /
b)
/
-*
11.0
8
f
7.5
--
Flgure 8. Empirical (a) and theoretlcal (b) values for the maximum concentration of available phosphate adsorption sites are compared. Again, the dashed lines depict a slope of 1 and an intercept of -AG,,,,,,,,.
in part be due to indiscriminant surface coordination at sites that were originally heterodisperse in terms of charge, rendering a more uniform charge distribution (37). How-
ever, an aggregation process, as postulated above, could also narrow the mobility distribution by mitigating the needlelike shape characteristic of monomeric goethite Environ. Sci. Technol., Vol. 19, No. 6, 1985
549
Mobility Histograms
with and without Adsorbed Phosphate
0
.
1
.
2
.
3
.
4
.
5
.
6
.
7
.
8
.
Mobility (ym.cm/V.sl
Figure 9, Electrophoretic mobility of goethlte shifts from an average of 4.58-1.71 pm-cm/(V.s) with the addition of 2.0 pM phosphate to 30 mg/L goethite at pH 5.71. As described under Materials and Methods, the goethite used here dlffered from that used for experiments summarized in Figure IC.
Frequency Spectro
with and without Adsorbed Phosphate 8.
-
7.
-
6. D
:
5.
$2
4.-
3 E
3. :
r:” o c
-
i
0
.”
5-1
w
1-
-
L 2.
.-
1.
I
I I I 1 I I t I
- 1.0
- .8
- .6
- .4
- .2
.O
.2
.4
.6
I
I .
I
, , . I
.8
1.0
Relative Frequency (HZ)
Figure 10. Frequency spectrum based on Brownian movement of the phosphated goethite is conslderably narrower than the phosphate-free spectrum. A narrower spectrum indicates that the particle size is larger.
crystals and increasing particle size, thereby limiting the range of Stokes’ friction values between various orientations of moving particles during electrophoresis. Analyzing the Brownian motion of goethite particles lends further support to an increase in particle size in the presence of phosphate. Larger particles exhibit less movement due to molecular collisions, and this is the case for phosphated goethite compared to phosphate-free particles (Figure 10). By use of eq 8-13 and Table I, the electrophoretic mobility of the phosphated goethite described in Figures 9 and 10 corresponds to a value of 1.6 kcaljmol for -AGelectrostatic. This value is greater than virtually all of the data presented in Figure 8, indicating that a larger, aggregated particle may characterize phosphated goethite slurries over a wide range of conditions. Conclusions Although it would be preferable to predict the maximum concentration of available adsorption sites from some a priori adsorbent characterization, this does not appear to be a feasible approach. Instead, empirical surface saturation results, similar to those presented in Figure 6, appear to be necessary in order to evaluate =(S1J, for each adsorbate species of interest. We feel that aggregation processes are responsible for the discrepancy between 550
Environ. Sci. Technol., Vol. 19, No. 6, 1985
theoretical determinations of the maximum site concentration and empirical results. Once a realistic value for (=S)total has been established, it is possible to model data obtained over a wide range of pH and adsorbate concentration with a single value for A G i n k i c (Figures 3b-5b). This apparently contradicts the opinion that separate intrinsic constants are necessary for each of the several combinations of pH-dependent conjugate acid forms of both the oxyanion and the goethite surface (3, 5, 6 ) . We have also demonstrated the ability to assign an electrostatic energy value based on an electrophoretic mobility measurement in conjunction with a pH determination (eq 8-13; Figures 3-5). Typically, the determination of electrostatic energy is based on an extensive calibration procedure using potentiometric titrations (5). Although theoretically sound, that approach is cumbersome in practice. Finally, we note that the relative magnitude of AGintrinsic influences the effect of electrostatics on anion adsorption. For the weakly bound sulfate ion electrostatic attraction can increase the amount adsorbed; however, the intrinsic energy of sulfate adsorption onto goethite is already too low to allow significant binding, and electrostatic repulsion cannot decrease the amount adsorbed in any meaningful sense. Therefore, sulfate is only bound at low pH values (Figures la-3a), and free energy data are difficult to obtain above pH 6 (Figure 3) because (=SA)becomes exceedingly small. Conversely, for the strongly bound phosphate ion, electrostatic repulsion can decrease the amount adsorbed; however, attraction cannot significantly increase coverage because the intrinsic energy is already high enough to cause nearly complete removal from solution. Therefore, phosphate is strongly bound except where pH and/or adsorbate concentration is high (Figures IC,2c, and 5a). Selenite has an intermediate value for AGintrinsic(Figure 4b), and the amount adsorbed is more readily affected by either electrostatic attraction or repulsion as environmental conditions change. Acknowledgments
We thank R. R. Stanforth and M. I. Tejedor-Tejedor for their technical assistance and are grateful to W. A. Zeltner for valuable discussions and critiques. We thank H. Grogan and J. Schneider for typing this manuscript. Registry No. Sulfate, 14808-79-8; selenite, 14124-67-5; phosphate, 14265-44-2; goethite, 1310-14-1.
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Receiued for review July 30,1984. Accepted January 11,1985. This research was funded by a grant from the Department of Energy under Contract DE-AC02-80EV10467.
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