Environ. Sci. Technol. 1991, 25, 395-403
Phosphorus Sorption by Sediments from a Soft-Water Seepage Lake. 1. An Evaluation of Kinetic and Equilibrium Models Naomi E. Detenbeck” and Patrick L. Breronik
Department of Civil and Mineral Engineering, University of Minnesota, Minneapolis, Minnesota 55455 Models describing kinetics and equilibria of sorption were compared by using phosphorus sorption data for sediments from Little Rock Lake (Vilas County, WI) at pH 4.5-6.0. A maximum sorption capacity was not exhibited by the sediments, but sorption continued to increase (slowly) as solution [Pi]increased. Sorption equilibria and kinetics thus did not fit well to simple models that assume homogeneous binding sites but were described by models that incorporate either a distribution of intrinsic binding energies or variable binding caused by a change in electrostatic potential with increasing surface coverage. The variance in sediment affinity for Pi described by current models (log K = 5.99 f 5.00) realistically cannot be ascribed solely to variation in intrinsic binding energies among different sites, but can be accounted for by a range in pHzpcvalues of 3 pH units. Sediments were slow to reach equilibrium (>54 h), especially at high pH and low initial Pi, consistent with a conceptual model of rapid adsorption followed by a period of intraparticle diffusion.
Zntroduction The effect of pH on phosphorus sorption by lake sediments must be adequately described in order to evaluate the potential role of acidification in lake oligotrophication ( I ) . To date, phosphorus sorption by lake sediments has been evaluated by using simple Langmuir isotherms to describe equilibrium conditions (2,3). Sorption data for sediments may not be adequately described by simple models derived for homogeneous surfaces, however ( 4 ) . Over the past decade, a variety of more complicated models have been developed that describe binding equilibria involving nonhomogeneous sites. To evaluate the effect of pH on inorganic P (Pi)sorption by sediments from Little Rock Lake (Vilas Country, WI), the site of a whole-basin acidification experiment, we investigated the statistical fit of five sorption equilibrium models of varying complexity and on kinetic model to our data. Sorption parameters were determined for sandy littoral sediments from three sites and for organic pelagic sediments from the deepest point of each of two basins of Little Rock Lake. Sorption was evaluated across the range of pH values (4.5-6.0) to be encountered during the experimental lake acidification. The effect of pH and sediment characteristics on phosphorus sorption by Little Rock Lake sedi-
* Present address: Natural Resources Research Institute, University of Minnesota, Duluth, MN 55811. 0013-936X/91/0925-0395$02.50/0
ments are described in detail elsewhere (5). Qualitative Models of Sorption Equilibrium. Early attempts to explain the effect of pH on ion sorption by heterogeneous surfaces were based on simple qualitative models. In most systems, the sorption of anions like phosphate decreases as pH increases and surface charge becomes more negative. Hingston et al. (6) observed a linear decrease in the apparent maximum sorption capacity of goethite for phosphate as pH increased (the sorption envelope), with a change in slope occurring at pK, values for H3P04(pK, = 7.2, pK3 = 12.3). He suggested that net surface charge and phosphate speciation determined the maximum sorption capacity of goethite as a function of pH; the high capacity of pH SS,,,.
well described by the BET model either (Figure 3b) and demonstrate a more gradual rise in sorption a t high Pi concentrations than this model predicts. Both the normal and quasi-normal distribution models provide a better fit to the data than do the Langmuir and BET models. The former models explain more than 90% of the variation in the data (Table 11; Figure 3c,d). Although the quasinormal model (eq 7) fits the data slightly better and is easier to use than the normal distribution models (eqs 8-10), the normal distribution is well characterized, and its dispersion parameter (a, the standard deviation) is easier to interpret than the index of heterogeneity (a) in the quasi-normal model. Perdue and Lytle (11) originally used h f 4a as limits of integration to evaluate the function 0 (log K ) in eq 8 but noted that the left half of the distribution has no effect on observed binding because the affinity associated with those sites is weak and site concentrations are low near the tail of the distribution. We used p f 40 as limits of integration in fitting the Perdue and Lytle model to Pi sorption data. However, in evaluating Barrow's model (eq 9), we used only the right half of the normal distribution of site concentrations (d\k,) to avoid generating computer overflow errors when evaluating the integral near the lower limit of integration. Barrow's equilibrium sorption model (Figure 3e) describes Pi sorption by Little Rock Lake sediments well, explaining 94% of the variation in sorption a t pH 4.5. In addition, Barrow's model allows one to predict the effects of pH by describing the initial potential as a function of pH. Panels a and b of Figure 4 show the estimated decrease in Q and \ka, respectively, as pH increases for pelagic sediments.
Discussion Patterns of Sorption Kinetics. Biphasic patterns (rapid sorption followed by a reduced rate of sorption) similar to those observed for Little Rock Lake sediments have been described for Pi sorption by goethite, gibbsite, and kaolinite (15,16,27) and for various soils (28). These patterns have been explained either as (i) an initial phase of sorption followed by fixation of Pi into crystalline phases such as variscite (A1P04.2H20)(27, 28) or octacalcium phosphate (Ca8H2(PO&5H,0) in soils (27) or as (ii) initial sorption of P, onto amorphous oxide surfaces, followed by absorption of surface Pi, Le., diffusion into the interior of particles (13).
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The first explanation of Pi sorption kinetics data (that initial sorption is followed by a slow phase corresponding to fixation) is not supported by phosphorus fractionation data for Little Rock Lake sediments (5). Little of the Pi in the sediments is found in Ca- or Fe-bound fractions, and the majority is in the easily exchangeable fraction. The minor Ca-bound fraction probably represents detrital P rather than the end product of diagenesis. In addition, fixation, had it occurred, would have led to a consistent final equilibrium concentration (independent of the amount of P, added) determined by a solubility product rather than by sorption equilibria (8). The empirical rate equations (12-24) described above also have been used to describe the biphasic kinetics of sorption. The Elovich equation (15) has been used to describe the isotopic exchange kinetics of Pi with goethite and gibbsite (16, 17). Equation 1 2 describes Pi sorption onto goethite (16) only for intermediate values of 0. The rapid initial phase of sorption by gibbsite also is described by this equation, but the subsequent slower phase of exchange is not (17). Chen et al. (27) described the slow phase of Pi sorption (at t > 24 h) by aluminum oxide and kaolinite as a first-order reaction, and based on X-ray crystallography, they suggested that this phase corresponds to nucleation and growth of AlP04 crystals similar to variscite. Barrow (18) found a similar pattern for calcareous soils but not for noncalcareous soils. Plots of Pi concentration vs time for calcareous soils at different initial Pi values converge to a common (equilibrium) concentration that can be predicted by the solubility product of octacalcium phosphate, Ca8H2(P04)6.5H20,again suggesting that the slow phase is controlled by crystal nucleation and growth. Data fitting Barrow's rate model (18) (eqs 13 and 14) can be plotted on a log-log scale to generate a function that is approximately linear (Figure 1). It is interesting to note that a semilog plot of eq 11 shows the pattern observed for Pi sorption by kaolinite (27); the plot approaches linearity as sorption increases. Thus, the general kinetics model could be used to describe both the rapid initial phase and the subsequent slower phase for Pi sorption by metal oxides, clays, soils, and sediments. If the general model (eq 11) is valid, Barrow's rate equation (eq 13) should apply only to systems with low surface coverage. This is true for Little Rock Lake sediments; average fractional surface coverage (0) is 10.2. Environ. Sci. Technol., Vol. 25,
No. 3, 1991 399
30 1
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When surface coverage is higher, as probably was the case for studies of Pi sorption onto goethite and gibbsite (15, 16), the Elovich equation should provide a better description of the data. Predicting pH Effects on Sorption from Surface Charge Characteristics. Barrow (29) found that the predicted initial electrostatic potential of a heterogeneous soil decreases as pH increases in the range 4-7, and the decrease is roughly linear with pH (-30 mV/pH unit). The standard deviation ( u ) of electrostatic potential also decreases as pH increases in the same range. Barrow noted that if the rate of change, d\k,,/dpH, were -10% lower, the model would predict no net effect of pH on sorption equilibrium. The effect of decreasing potential would be offset by an increase in the proportion of Pi present as more highly charged (divalent) HPOd2-. When Barrow (29) applied his equilibrium model to a variety of soils with different phosphate levels, a more complex pattern of pH effects emerged. The initial po400
Environ. Sci. Technol., Vol. 25, No. 3, 1991
tential, QaO,consistently increased as pH decreased between pH 7 and 3 in all cases, but for previously fertilized soils, the rate of increase in potential was not sufficient to offset changes in phosphate speciation. In addition, u did not consistently decrease as a function of pH for all soils. The effect of pH on u was related to soil buffering capacity; u increased at low pH for soils with a relatively high buffering capacity but decreased at low pH for soils with a relatively low buffering capacity. If a constant capacitance (capacitance = Q / 9 )model is assumed (30),the change in mean \k, with pH for Little Rock sediments could be predicted from plots of excess surface charge, Q, vs pH. Given the almost linear decrease in Q with pH for the pelagic sediments (Figure 4a), 9, should decrease linearly with pH. Because the sediments had a low surface coverage initially, it is not the average value of but values of 9, near the right tail of the probability distribution of site concentrations (dq,,) that will affect sorption of added Pi. The highest values of 9,corresponding to available sites can be determined by adding the appropriate number of standard deviations to the average 9,for a given coverage, 8. Predicted values of 9,near the tail of the distribution (9ao + 2u - m,B) decrease with pH for the pelagic sediments but in a curvilinear fashion (Figure 4b). This implies that the net effect of pH on Pi sorption by heterogeneous sediments cannot be modeled solely on the basis of sediment titration curves and subsequent calculation of excess surface charge. Instead, changes in both the mean and variance of \k, with pH influence Pi sorption. A decrease in u can offset an increase in mean potential. Plots of Q vs pH reflect changes in only auerage potential. Sources of Variability in Affinity for Pi within Sediments. Variance in the affinity for Pi among sites within Little Rock Lake sediments can be explained partly by differences in the pH at which sediment sites have zero potential charge, i.e., the pH, ,values. Sites with a pH,,, of 6.2 or higher will be positiveyy charged over the pH range of interest. (Porewater pH of Little Rock Lake sediments varies over the range 4.7-6.2.) Thus, those sites with higher pH,,, values can be expected to bind Pi more efficiently at low Pi concentrations, i.e., approach a maximum sorption capacity more quickly as Pi is added. The relative shape of the isotherms is determined not only by the sorption maximum and average sediment affinity for phosphate, but also try the degree of variation in binding energy. Although the Perdue and Lytle model fits the data well, the range of log K values estimated is very large compared with known values of binding constants for iron oxides. Bowden et al. (25) measured a binding constant of 1.4 X lo7L/mol P for HPOt- sorption onto pure goethite (log K = 7.15) compared with a range of log K of 0-10 ( p f 2u) predicted for 95% of sites in Little Rock pelagic sediment by the Perdue and Lytle model (Table 11). Although the porosity of iron oxides appears to affect their affinity for phosphate, this probably does not account for more than 1 order of magnitude of the variation in affinity, Le., 1 log K unit (31). A possible source of variation in binding constants in addition to porosity and variation of pH,,, is the form of Fe in the sediments. Some of the sedimentary Pi may be bound to Fe complexed to humic acids (HA) or fulvic acids (FA) (32). In soils, the amount of Pi associated with soil FA-metal complexes increases with A1 or Fe content (33). According to Senesi et al. (34,initial additions of Fe3+to soil HA and FA are strongly bound in tetrahedral or octahedral sites protected from inorganic ligands, whereas subsequent additions of Fe3+ are weakly bound (sorbed)
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Figure 3. Equilibrlum sorption data for sediment SP1 at pH 4.5 plotted according to (a) Langmuir model, (b) BET model, (c) Sips quasi-normal model, (d) Perdue and Lytle normal distribution model, and (e) Barrow's sorption equilibrium model.
onto the surface of organic acids and are available for the formation of complexes with inorganic ligands. The affinity of iron-organic acid complexes for Pi thus depends upon the type of organic site involved. Equilibrium constants (log K ) for mixed two-ligand complexes of the type M-Oc-Pi (where M = Al, Zn, or Cd, 0, = various simple organic anions, and Pi = phosphate) vary over a range of -3.4 log units (35-37). Unfortunately, the range of affinities between phosphate and Fe or A1 complexed with naturally occurring organic matter is unknown. For surfaces characterized by the Nernst equation, the initial potential (QQo) varies with pH (6\kQo/6pH= 59), and the standard deviation (a) of \kQodepends on the range in pH,,, values for different sites. However, when Barrow (13)fit his model to a heterogeneous soil, the model actually predicted a decrease in initial potential of only 30 mV per unit pH increase. Barrow estimated a mean initial potential of -72 mV and a of 50 mV for the soil at pH 5.6. The range of pH,,, values of individual sites required to explain 95% of the variation (-2a) in the right half of the
distribution for QQOwould be (50 X -2)/30 = -3.3 pH units, which is a reasonable range of variation. Thus, the range in binding intensities required to model sorption by soils or sediments is greater than that expected for intrinsic binding constants alone, but can be accounted for by solid-phase components with pH, values ranging over -3 pH units. In fact, both intrinsic binding constants and electrostatic potentials probably vary among sites, but much of the variance in binding can reasonably by accounted for by differences in electrostatic potential (pHv). Conclusions Equilibria and kinetics data for Pi sorption by Little Rock Lake sediments do not fit well to simple models that assume homogeneous binding sites (B), but are well described by models that incorporate either a distribution of intrinsic binding energies (10,12) or variable binding caused by a change in electrostatic surface potential (13). While equilibrium sorption data for pelagic sediments from Little Rock Lake can be described by Perdue and Lytle's Environ. Sci. Technol., Vol. 25, No. 3, 1991
401
Acknowledgments We thank Gregg Downing for providing information on metal fractions of sediments from Little Rock Lake, Leslie Sherman for providing assistance with Marquardt’s nonlinear least-squares fitting routine, and the Elaine Helmer for helpful discussions of binding models.
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+
Gaussian model, which incorporates variation in intrinsic binding energies among different sites (12),the range in binding energies predicted, log K = 0-10 (w f 2u), is unrealistic. Differences in binding energy due to porosity of iron oxides and/or to variation in intrinsic Ki can reasonably account for a range of only a few log K units. However, the range of apparent binding intensities can be accounted for by variation in both Ki and electrostatic potential, qa.For example, the variance in \k, determined by Barrow for a heterogeneous soil could be accounted for by sites with pHzpcvalues varying over approximately 3 pH units. The biphasic pattern of sorption kinetics (rapid initial sorption followed by a reduced rate of sorption) observed by other investigators for Pi sorption by various minerals and soils (15,16,28) is also observed for Little Rock Lake sediment, particularly at low pH. The hypothesis that the latter phase of slow sorption corresponds to fixation in a mineral phase (27,28) is not consistent with the low levels of Ca- or Fe-bound Pi extracted from Little Rock Lake sediments. However, fixation can occur in soils or sediments with higher Ca, Al, or Fe contents than Little Rock Lake sediments, as in the calcareous soils investigated by Barrow (29). The pattern of sorption kinetics observed is consistent with a general rate equation that incorporates variation in activation energy with changing coverage, 8 (14). The general rate equation developed by Aharoni and Ungarish is consistent with Barrow’s rate model at low coverage (0) and with the Elovich model at intermediate coverage values. Similarly, the biphasic pattern of sorption kinetics can be explained by Barrow’s equilibrium sorption model with a term added for intraparticle diffusion (13). 402
Environ. Sci. Technol., Vol. 25, No. 3, 1991
Literature Cited Grahn, 0.; Hultberg, H.; Landner, L. Ambio 1974, 3, 93. Ogburn, R. W., 111; Brezonik, P. L. Water, Air, Soil Pollut. 1986, 30, 1001. Mayer, T.; Kramer, J. R. Water, Air, Soil Pollut. 1986,31, 949. Hingston, F. J. In Adsorption of Inorganics at Solid-Liquid Interfaces; Anderson, M. A., Rubin, A. J., Eds.; Ann Arbor Science: Ann Arbor, MI, 1981; Chapter 2. Detenbeck, N. E. Ph.D. Dissertation, University of Minnesota a t Minneapolis, 1987. Hingston, F. J.; Atkinson, R. J.; Posner, A. M.; Quirk, J. P. Nature 1967, 215, 1459. Edzwald, J. K. In Fate of Pollutants in the Air and Water Environment; Suffet, I. H., Ed.; Adu. Environ. Sci. Technol. 1977, 8 , 183. Brunauer, S.; Emmet, P. H.; Teller, E. J . Am. Chem. SOC. 1938, 60, 309. Dzombak, D. A.; Fish, W.; Morel, F. M. M. Environ. Sci. Technol. 1986, 20, 669. Nisonoff, A.; Pressman, D. J . Immunol. 1958, 80, 417. Sips, R. J . Chem. Phys. 1948, 16, 490. Perdue, E. M.; Lytle, C. R. Enuiron. Sci. Techno!. 1983, 17, 654. Barrow, N. J. J . Soil Sci. 1983, 34, 733. Aharoni, C.; Ungarish, M. J . Chem. SOC.,Faraday Trans. 1976, 73, 456. Allen, J. A.; Scaife, P. H. Aust. J . Chem. 1966, 19, 2015. Atkinson, R. J.; Posner, A. M.; Quirk, J. P. J . Inorg. Nucl. Chem. 1972,34, 2201. Kyle, J. H.; Posner, A. M.; Quirk, J. P. J . Soil Sci. 1975, 26, 32. Barrow, N. J. J . Enuiron. Qual. 1980, 9, 644. Olsen, S. R.; Sommers, L. E. In Methods of Soil Analysis. Part 2. Chemical and Microbiological Properties; 2nd ed.; American Society of Agronomy and Soil Science Society of America: Madison, WI, 1982. Laverdiere, M. R.; Weaver, R. M. Soil Sci. SOC.Am. J. 1977, 41, 505. Standard Methods f o r the Analysis o f Water and Wastewater, 15th ed.; APHA, WPCF, AWWA: Washington, DC, 1981. Sibanda, H. M.; Young, S. D. J . Soil Sci. 1986, 37, 197. Schreiner, M.; Kramer, M.; Drischer, S.; Langsam, Y. PC Tech. J . 1985, (May), 170. Standard Mathematical Tables, 23rd ed.; Selby, E. M., Ed.; CRC Press: Cleveland, OH, 1975. Bowden. J. W.: Naearaiah. S.: Barrow. N. J.: Posner, A. M.; Quirk, J. P. Aust.-J. i o i i Res. 1980,’18, 49. Kenney, R. Water Resour. Res. 1982, 18, 1041. Chen, Y. S. R.; Butler, J. N.; Stumm, W. Environ. Sci. Technol. 1973, 7, 327. Munns, D. N.; Fox, R. L. Soil Sci. SOC.Am. J . 1976,40,46. Barrow, N. J. J . Soil Sci. 1984, 35, 283. Morel. F. M. M.: Westall. J. C.: Yeasted, J. G. In Adsorption of Inorganics at Solid-Liquid Interfaces; Anderson, M. A., Rubin, A., Eds.; Ann Arbor Science: Ann Arbor, MI, 1981; Chapter 7 . Madrid, L.; De Arambarri, P. J . Soil Sci. 1985, 36, 523. Francko, D. A.; Heath, R. T. Limnol. Oceanogr. 1979,24, 463. Schnitzer, M. Soil Sci. SOC.Am. Proc. 1969, 33, 75. Senesi, N.; Griffith, S. M.; Schnitzer, M. Geochim. Cosmochim. Acta 1977, 41, 969. Ramamoorthy, S.; Manning, P. G. J . Inorg. Nucl. Chem. 1973, 35, 1571.
Environ. Sci. Technol. 1991, 25,403-409
(36) Ramamoorthy, S.; Manning, P. G. J . Inorg. Nucl. Chem. 1974, 36, 695. (37) Ramamoorthy, S.; Manning, P. G. J . Inorg. Nucl. Chem. 1975, 37, 363.
Received for review December 7, 1989. Revised manuscript
received August 21,1990. Accepted October 12,1990. This work was supported in part by a cooperative agreement with the US. EPA (Duluth Environmental Laboratory),J. G. Eaton, project officer. I t has not been reviewed by the EPA for technical merit or policy implications, and no official endorsement should be inferred.
Phosphorus Sorption by Sediments from a Soft-Water Seepage Lake. 2. Effects of pH and Sediment Composition Naomi E. Detenbeck" and Patrick L. Breronik Department of Civil and Mineral Engineering, University of Minnesota, Minneapolis, Minnesota 55455
The effects of pH and sediment composition on phosphorus sorption by sandy littoral and organic-rich pelagic sediments from Little Rock Lake (Vilas County, WI) were evaluated in laboratory experiments. About two-thirds of total sedimentary P is in organic forms. Concentrations of inorganic P (Pi)are low in littoral sediments (0.66-1.71 pmol/g). In pelagic sediments Pi concentrations are approximately 10 times higher (16.1-19.4 pmol/g). Most of the Pi (-70%) is readily exchangeable. Variability in Pi is related to surface area and aluminum oxyhydroxide content but not to iron oxyhydroxides. Potential effects of pH on sorption are large; predicted equilibrium phosphate concentrations (EPC) decrease by 88-91 % between pH 6.0 and 4.5, as P binding by the sediments increases. Diffusive fluxes of Pi out of the sediments could decrease by as much as 90% if surficial sediments in Little Rock Lake become acidified. Introduction
The importance of lake sediments in regulating phosphorus cycling has been known for many years. Exchangeable phosphorus content and sorption capacities have been correlated with sediment compositional characteristics such as iron, aluminum, and organic matter content (I-3),and in turn, sediment composition has been related (qualitatively) with lake chemistry, i.e., with hardness, alkalinity, and pH (4). Laboratory studies on soils and pure minerals have shown that phosphorus sorption varies with pH ( I , 5 ) , but little information is available on the direct effects of p H on phosphorus sorption by lake sediment, especially within the pH range of interest for sediments from low-alkalinity (acid-sensitive) lakes, i.e., pH 4.5-6.0. These effects are of interest with regard to the consequences of acidification for phosphorus cycling in lakes, and this issue bears on the hypothesis that acidification induces lake oligotrophication (6). The effects of pH on lacustrine phosphorus cycling depend in part on the direct, short-term effects of pH on sorption equilibria and kinetics, as well as on the long-term effects of acidification on organic mineralization rates and on sediment composition. Phosphorus sorption by sediment from a clear-water acidic lake in Florida was found to increase with decreasing solution pH over the range 6.0-3.5, and the increase in sorption was greatest in the range 5.5-4.5 (7). However, results of this study are insufficient to determine sorption isotherm parameters. More recently, Mayer and Kramer
* Present address: Natural Resources Research Institute, University of Minnesota, Duluth, MN 55811. 00 13-936X/9 1/0925-0403$02.50/0
(8) compared sorption isotherms for calcareous and noncalcareous lake sediments as a function of pH. Although sorption increased as pH decreased for a given sediment, the authors concluded that sediment composition was more significant than pH in affecting phosphorus sorption. In order to predict the effects of lake acidification on phosphorus cycling, however, the factors controlling phosphorus sorption within a given lake and the effects of pH on sorption to a given sediment are more important than differences among lakes. Our study was designed to model the short-term effects of pH on phosphorus sorption by sandy and organic sediments from a dilute, low-alkalinity lake, Little Rock Lake (Vilas County, WI), as well as to describe the factors controlling the variability of exchangeable phosphorus in the lake's sediments. Methods
Study Site. Little Rock Lake, a small (18 ha), two-basin seepage lake in north-central Wisconsin, is the site of an ongoing whole-basin acidification experiment (9). Its watershed is wholly forested, and surrounding soils are highly permeable glacial till. The lake water is highly dilute (conductivity 11pS/cm, alkalinity 25 pequiv/L, pH = 6.0). Physical and chemical characteristics of the lake's sediments were measured before acidification of the north basin began ( I O , I I ) , and few interbasin differences were found, except for those related to water depth. Sandy littoral sediments occupy -30% of the lake area. They contain 1-25% organic matter, and their inorganic fraction is mostly made up of sand-sized particles (88-98%). The transition between littoral sediments (organic matter content
