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Geoderma xx (2

OF

Sulphate sorption at high equilibrium concentration in Andosols

Thomas Delfosse a,⁎, Pierre Delmelle b, Bruno Delvaux a

a Unité des Sciences du Sol, Université catholique de Louvain, Place Croix du Sud, 2/10, 1348 Louvain-la-Neuve, Belgiumb Environment Department, University of York, Heslington YO10 5DD, York, United Kingdom

Received 23 December 2004; received in revised form 15 March 2006; accepted 3 May 2006

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Abstract

Themain process bywhich inorganic SO42− inputs are retained in soils is through adsorption on soil colloids.However, in soils subject

to intense SO42− addition, precipitation of Alx(SO4)y(OH)zminerals alsomay contribute to SO4

2− sorption.While direct observation of Alx(SO4)y(OH)z precipitate in soil has been reported only recently, SO4

2− sorption isotherms experiments have been rarely performed todistinguish between adsorption and precipitation processes.

Traditionally, SO42− sorption experiments have involved relatively lowSO4

2− concentrations in the range 0–5mM.However, for SO42−

precipitation to occur, higher concentrations may be needed. Here, we evaluated SO42− sorption in four contrasting Andosols samples by

measuring sorption isotherms with SO42− concentrations ranging from 0.1 to 15 mM and under low pH conditions (pH 4). A 1 h sorption

equilibration time was allowed. All sorption isotherms showed a distinct biphasic shape. In the lowest SO42− concentration range

(b5 mM), SO42− sorption obeyed a Langumir isotherm, whereas at higher SO4

2− concentrations (N6 mM), SO42− sorption could be

described by a linear isotherm. The transition between a Langmuir-type and a linear-type isotherm also corresponded to the transitionpoint where the solution was oversaturated with respect to Alx(OH)y(SO4)z minerals, according to thermodynamic calculations. Weinterpreted these results in terms of initial SO4

2− adsorption onto the surface of soil constituents at lower dissolved SO42− concentrations

followed by SO42− precipitation at high dissolved SO4

2− concentrations.© 2006 Elsevier B.V. All rights reserved.

E RKeywords: Sulphate sorption; Soil anion adsorption; Andosols; Alunite supergroup; Biphasic isotherm

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R1. Introduction

Sulphate (SO42−) may accumulate in soils exposed to

high S inputs through various processes, including (i) im-mobilization as organic S (Prietzel et al., 2004), (ii) adsorp-tion on mineral surface, (iii) precipitation in a Alx(SO4)y(OH)z mineral phase (Adams and Rawajfih, 1977; Prietzeland Hirsch, 2000) and (iv) irreversible migration of ionsinto short range-ordered minerals, i.e. occlusion (Delfosseet al., 2005a). Althoughmost of the inorganic SO4

2− in these

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⁎ Corresponding author. Tel.: +32 10 47 36 38; fax: +32 10 47 45 25.E-mail address: delfosse@sols.ucl.ac.be (T. Delfosse).

0016-7061/$ - see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.geoderma.2006.05.009

soils tends to be retained by an adsorption mechanism,precipitation also may contribute to SO4

2− sorption for asignificant part (Prietzel and Hirsch, 2000; Delfosse et al.,2005a,c).

The presence of Alx(SO4)y(OH)z mineral in S-impac-ted soils has been suspected for a long time (Adams andRawajfih, 1977; Prietzel and Hirsch, 2000). However,direct observation of a Alx(SO4)y(OH)z phase in soil hasproven to be difficult, and it is only recently that it wasidentified on clay soil particles of Andosols (Delfosseet al., 2005c). The lack of previous evidence probablyoriginates from inappropriate methodology, but also be-cause adsorption and precipitation mechanisms can rarely

GEODER-02645; No of Pages 7

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be distinguished experimentally (McBride, 2000). Themajor difference between the two processes lies in thatadsorption is two-dimensional, whereas precipitation isthree-dimensional. In fact, the uptake of adsorbate ions bysoil, which is termed sorption, can be viewed as a con-tinuous process, which ranges from adsorption at lowadsorbate concentration, to precipitation at higher adsor-bate concentration (McBride, 2000).

In general, SO42− sorption in soils is investigated as a

function of equilibrium SO42− solution concentration typi-

cally in the range∼0–5mM.These conditions have led tosorption maxima of ∼1100 mg S kg−1 (e.g. Haque andWalmsley, 1973; Singh, 1984; Curtin and Syers, 1990),and adsorption was inferred to dominate SO4

2− sorption.However, in areas affected by strong S inputs, such asthose originating from deposition of marine aerosols or ofvolcanic gases and particles, comparatively higher SO4

2−

concentrations in soil solution may occur. Under suchconditions, the total soil SO4

2− content sometime exceeds5000 mg S kg− 1 (Hasan et al., 1970; Hue et al., 1990;Takamatsu et al., 1992). Several studies have highlightedthat S storage in these environments may be drawn bySO4

2− precipitation (Hue et al., 1990; Takamatsu et al.,1992; Delmelle et al., 2003; Delfosse et al., 2005b,c),possibly leading to the formation of a Alx(SO4)y(OH)zmineral phase (Adams and Rawajfih, 1977; Nordstrom,1982). In Andosols affected by large volcanogenic Sdeposition, precipitation was shown to account for up to50% of total soil SO4

2− content (Delfosse et al., 2005c).This calls for a better understanding of SO4

2− sorption athigh concentrations in soils. Towards this aim, we carriedout SO4

2− sorption isotherms at high dissolved SO42− con-

centrations on four Andosols samples, which displaycontrasting weathering stages.

To a certain extent, the shape of a sorption isothermprovides insights into adsorbate–adsorbent interactions,and isotherms have been classified into four types (L-, H-,C- and S-type) (Giles et al., 1974). The S-type (convexshape) isotherm suggests “cooperative adsorption”, littleadsorption occurs at low concentrations and increasesprogressively as the concentration is raised. Type C(constant-partitioning) isotherm, is generally linear andsuggests a constant relative affinity of the adsorbatemolecules for the adsorbent. Type L (Langmuir) and H(High affinity) represent Langmuirian adsorption iso-therms, i.e. it presents a decreasing slope as concentra-tion increases due to the saturation of available sites. H-type indicates stronger adsorbate–adsorbent interactionsthan L-type isotherms. Detailed descriptions of this clas-sification are given in Giles et al. (1974) and McBride(2000). We used this classification to interpret ourresults.

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2. Materials and methods

2.1. Soils

Soil samples were collected in the vicinity of Masayavolcano (Nicaragua), one of the world strongest sourcesof SO2 to the atmosphere (Delmelle et al., 2001). This areais covered with Andosols developed from successivebasaltic tephra layers, with remarkably uniform chemicalcomposition (Walker et al., 1993). A previous study in-dicated that the Andosols differ by their weathering stage(Delfosse et al., 2005b). Young and comparatively lessweathered profiles (Vitric series; VI) are located within5 km from the volcano, whereas more weathered soils(Eutric series; EU) are found farther downwind (see Del-fosse et al. (2005b) for details on soil locations and majorproperties). The Masaya Andosols have experienced along-history of strong S deposition, resulting in excep-tional S accumulation ranging from 680 to 5470 mg totalS kg−1 soil (Delmelle et al., 2003).

2.2. Sulphate sorption isotherms

Sulphate sorption isotherms were performed on fourAndosol horizons (labelled EU2-Bw, EU5-A2, EU9-A2and VI2-3A) representing the Eutric and Vitric soil pro-files found in the Masaya area. These samples were se-lected on the basis of their contrasting short-range orderedmineral and KH2PO4-extractable SO4

2− contents. Short-range ordered minerals are ∼10 times more abundant inthe well-developed EU2-Bw sample than in the undiffer-entiated VI2-3A sample. EU5-A2 and EU9-A2 soils havesimilar mineralogical properties, but they differ by theirKH2PO4-extractable SO4

2− contents. The soil major pro-perties are summarized in Table 1. We carried out SO4

2−

sorption isotherms in acidic conditions at 20 °C, byshaking 3 g of soil with 50 ml Na2SO4 solution withconcentrations 0.1, 0.5, 1, 2, 3, 4, 5, 6, 7.5, 10, 12 and15 mM SO4

2−. Solutions were initially acidified to pH 4with HNO3 and contained 0.1 M KNO3 as supportingelectrolyte to keep the ionic strength constant. The initialpH condition roughly corresponds to that observed for theacid rain collected in the Masaya area (Delmelle et al.,2003). Reaction between SO4

2− solution and soil samplewas allowed to proceed for 1 h with continuous stirring.The soil–solution mixture pH was kept constant at pH 4by adding 0.4 M HNO3 with an automatic titrator. Thesuspension was then centrifuged, filtered (Whatman41 filter) and analysed for SO4

2−. Cations and Al weredetermined by Inductively Coupled Plasma–AtomicEmi-ssion Spectrometry (ICP–AES), whereas anion concen-trations were obtained by ion chromatography (IC). For

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t2:1

t2:2

t2:3

t2:4

t2:5

t2:6

t2:7t2:8

t2:9

t2:10

t2:11t2:12

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t2:24

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t2:26t2:27

t2:28

Table 1t1:1

pH and CEC# values, carbon contents (Org. C), oxalate (o)§ extractable contents, Total Reserve in Bases¶ (TRB), specific surface (Sm)†, KH2PO4 (p)

extractable SO42− of the four Andosols samples studied in the sorption isotherm (adapted from Delfosse et al., 2005a,b)t1:2

t1:3 Profile Horiz. Depth pH Org. C CEC Sio Feo TRB Sm SO42−

p

t1:4 (cm) H2O (%) (cmolc kg−1) (g kg−1) (g kg−1) (cmolc kg

−1) (m2 g−1) (g kg−1)

t1:5 EU2 Bw 29–39 5.3 5.8 21.8 41.5 65.4 199 308 3.03t1:6 EU5 A2 5–16 6.9 5.1 36.9 19.4 27.1 396 170 0.04t1:7 EU9 A2 6–24 5.7 4.7 21.5 19.0 29.2 400 163 0.45t1:8 VI2 3A 14–24 4.9 2.0 7.8 5.3 8.5 530 83 0.76

# CEC measured by the BaCl2 method (Hendershot and Duquette, 1986).t1:9

§ Oxalate extractable contents of Si and Fe determined according to Dahlgren (1994).t1:10

¶ The Total Reserve in Bases (TRB) is the sum of total Na, K, Ca andMg and estimates the content of weatherable minerals in soils (Herbillon, 1986).t1:11† measured by the ethylene glycol monoethyl ether (EGME) method (Carter et al., 1965).t1:12

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these experimental conditions, biological immobilizationwas considered negligible (Houle et al., 2001). Sorptionexperiments were done in duplicate. Sorbed SO4

2− wascalculated from the difference between the initial andequilibrium SO4

2− concentrations, after correction for en-trapped solution. The amount of OH− released was deter-mined from the amount of HNO3 consumed to maintain aconstant pH value of 4.

3. Results and discussion

All isotherms exhibited a biphasic shape: character-ized by a L-type shape (Langmuir-like; Giles et al.,

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Table 2Content of SO4

2− sorbed, OH− released, and Al concentrations in the equilib

Sample SO42− added SO4

2− sorbed OH− released Al in solution Sa

(mmolc kg−1) (mmolc kg

−1) (mmolc kg−1) (mmolc l

−1)

EU2-Bw 3.3 −1.1 91.4 1.0 EU16.0 8.4 104.8 1.133.0 19.6 107.2 1.168.8 39.0 116.9 1.1

101.0 49.8 116.4 1.0136.2 60.0 120.2 1.0164.6 64.3 116.7 0.9196.0 68.4 126.0 1.0251.3 76.8 135.0 1.1335.8 100.9 140.4 1.1401.8 115.4 149.3 1.0512.2 140.3 158.7 1.2

EU5-A2 3.3 0.8 177.3 0.2 V16.0 5.0 174.2 0.233.0 9.3 179.0 0.268.8 15.2 178.2 0.2

101.0 21.2 190.1 0.2136.2 21.9 184.9 0.3164.6 23.4 189.2 0.2196.0 24.5 187.1 0.2251.3 27.9 183.1 0.3335.8 43.0 193.8 0.3401.8 55.5 198.7 0.3512.2 67.6 207.0 0.3

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lower than 5 mM and a C-type (linear) shape at higherconcentrations (N6 mM). The transition between the twocurves was characterized by an abrupt change in slope.Statistical analysis showed that the slopes of the L-typeand the C-type isotherms at the transition point differedsignificantly, indicating that sorption at high SO4

2−

concentration departed from that at lower SO42−

concentration. This biphasic isotherm suggests thattwo SO4

2− sorption mechanisms were involved: one overlow SO4

2− concentrations in equilibrium solution(b5 mM), and one over higher range. We discuss themseparately.

TErium solution as a function of SO4

2− added

mple SO42− added SO4

2− sorbed OH− released Al in solution

(mmolc kg−1) (mmolc kg

−1) (mmolc kg−1) (mmolc l

−1)

9-A2 3.3 0.2 76.4 0.716.0 4.7 83.3 0.833.0 9.6 82.8 0.868.8 15.9 94.7 0.8101.0 19.9 93.2 0.8136.2 22.5 91.0 0.8164.6 24.3 88.8 0.8196.0 25.1 89.1 0.9251.3 31.3 97.1 0.8335.8 46.2 100.4 0.9401.8 61.0 112.3 0.9512.2 79.5 115.6 1.0

I2-3A 3.3 −2.2 22.8 0.716.0 −0.3 18.9 0.633.0 2.7 18.2 0.668.8 3.5 22.9 0.6101.0 4.9 20.2 0.6136.2 6.4 23.3 0.7164.6 9.4 25.8 0.6196.0 10.5 23.8 0.6251.3 11.9 30.5 0.7335.8 23.9 29.9 0.7401.8 35.7 33.2 0.7512.2 46.1 37.5 0.7

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3.1. Sulphate sorption and soil constituents

The L-type shape isotherm describing SO42− sorption

on the four Masaya Andosols at low SO42− concentra-

tions (b5 mM) is consistent with previous studies onother soil types (e.g. Rajan, 1979; Curtin and Syers,1990). In this case, the L-type shape suggests an ad-sorption process with a maximum in SO4

2− sorptionoccurring at∼5 mM SO4

2− in equilibrium concentration.This maximum indicates saturation of the soil's availablesorption sites. In addition, for all samples, SO4

2− sorptionresulted in OH−release (Table 2) suggesting that SO4

2−

exchangewith surficial OH− groups occurred at low SO42−

solution concentrations in these Andosols. As reportedby Curtin and Syers (1990) on other tropical soils, thesorption of SO4

2− in our samples was also associated withcation adsorption (mainly K+) that maintains the chargebalance at the adsorbing surface.

As shown in Fig. 1, SO42− sorption was systematically

higher for EU2-Bw over the entire concentration range,and decreased in the order EU2-BwNEU9-A2=EU5-A2NVI2-3A. This probably reflects the larger short-rangeorderedmineral content in EU2 soil as compared to that inthe other soil samples (Table 1). It has been shownelsewhere (e.g., Fuller et al., 1985; CampsArbestain et al.,1999) that the extent of SO4

2− sorption in soils is dictatedmainly by Al and Fe oxyhydroxide contents.

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Fig. 1. Sorption isotherms of sulphate by fou

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3.2. Sorption–precipitation continuum

Although SO42− sorption in soils has been the subject

of many studies, only a few of them have reported on thebiphasic shape of the SO4

2− sorption isotherm at highequilibrium SO4

2− concentration (e.g. Barrow, 1967;Aylmore et al., 1967). Interestingly, a similar behaviourhas been observed for phosphate (PO4

3−) sorption insoils (e.g. Bache, 1964; Farley et al., 1985; Li andStanforth, 2000). In these biphasic PO4

3− sorption iso-therms, the second part of the curve corresponding tohigh anion concentration in solution has been inter-preted in terms of (i) occurrence of additional bindingsites on the soil constituents for adsorption (Aylmoreet al., 1967); (ii) occlusion of anion within amorphous orsemi-crystalline minerals (Muljadi et al., 1966); and (iii)surface-cataysed precipitation (Bache, 1964; Farleyet al., 1985; Li and Stanforth, 2000). These hypothesesalso may apply in the case of SO4

2− sorption since similarbinding sites are thought to be involved in the adsorp-tion of SO4

2− and PO43− (Parfitt, 1978).

Adsorption of SO42− on another pool of binding sites

should result in a secondary L-, H- or S-type isotherm(Giles et al., 1974), since the newly available sites will beprogressively saturated at high SO4

2− concentration insolution. This process cannot account for the linear iso-therm shape that we observed (Fig. 1).

T

r Andosol samples of the Masaya area.

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Table 3 t3:1

Saturation indices for alunite, basaluminite and jurbanite in function ofadded SO4

2− obtained by applying the PHREEQC chemical equilibriacode (Parkhurst and Appelo, 1999) t3:2

t3:3SO42− added Saturation indices

t3:4Alunite Basaluminite Jurbanite

t3:5(mmolckg−1)

KAl3(OH)6(SO4)2

Al4(OH)10(SO4)·5H2O

Al(OH)(SO4)·5H2O

t3:6EU5-A2 3.3 2.98 −2.95 −0.69t3:733.0 3.17 −3.88 −0.51t3:868.8 3.48 −3.74 −0.15t3:9101.0 3.97 −3.61 −0.07t3:10164.6 4.29 −3.05 0.13t3:11251.3 4.57 −3.80 0.30t3:12EU2-Bw 3.3 4.66 −1.35 −0.19t3:1333.0 4.76 −1.30 −0.06t3:1468.8 5.44 −1.24 0.13t3:15101.0 5.58 −1.18 0.21t3:16164.6 5.84 −1.35 0.60t3:17251.3 6.33 −1.32 0.84t3:18EU9-A2 3.3 4.12 −2.03 −0.37t3:1933.0 4.81 −1.65 −0.04t3:2068.8 5.45 −1.85 0.34t3:21101.0 5.60 −1.50 0.49t3:22164.6 5.90 −1.52 0.65t3:23251.3 6.01 −1.86 0.81t3:24VI2-3A 3.3 4.55 −2.64 −0.39t3:2533.0 4.62 −2.16 −0.03t3:2668.8 5.29 −2.06 0.23t3:27101.0 5.36 −2.01 0.44t3:28164.6 5.56 −2.09 0.58t3:29251.3 5.66 −2.47 0.72

Positive values denote oversaturation, whereas negative values in-dicate undersaturation. t3:30

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Occlusion of SO42− within amorphous or semi-

crystalline minerals also can be discarded. The amountof occluded material into a particle is a function of time,and is linearly dependent on the volumetric concentrationof the ion at the particle surface (Cis) (Crank, 1975). Inthe equilibration experiments, time is a constant factorand Cis is the only variable. Therefore, there should be alinear relationship between the volumetric concentrationof SO4

2− and the amount of SO42− potentially sorbed by

occlusion over the entire concentration range. AdditionalSO4

2− sorbed by adsorption should lead to an isothermslope equal or superior to that displayed by the linearportion of the isotherm. In our experiments, the slope ofthe transition between L-and C-type isotherms was closeto zero, indicating that SO4

2− occlusion does not accountfor such sorption process.

The most likely explanation for the biphasic nature ofthe SO4

2− sorption isotherm is precipitation of SO42− in a

mineral phase. This mechanism has been recentlyinvestigated by Li and Stanforth (2000) to explain thebiphasic nature of isotherms obtained for PO4

3− sorptionon goethite. Occurrence of SO4

2− precipitation at highdissolved SO4

2− concentration is also consistent with theidentification of basic aluminium sulphate minerals inthe S-rich Vitric Andosols of the Masaya area (Delfosseet al., 2005c).

The occurrence of SO42− precipitation during sorption

experiment is also supported by thermodynamic calcula-tions. PHREEQC code was used to predict saturation ofthe experimental equilibrium solution with respect tomineral phases (Parkhurst andAppelo, 1999). Calculationresults indicated oversaturation with respect to jurbaniteAlSO4(OH)·5(H2O) at a SO4

2− concentration in equilib-rium solution above ∼0.5–2.5 mM (Table 3), andundersaturation with respect to this mineral at lowerconcentrations. The concentration at which oversaturationwas detected corresponded approximately to the transi-tion between the L- and C-type isotherms. PHREEQCalso predicted oversaturation with respect to alunite KAl3(SO4)2(OH)6 and undersaturation with respect to basalu-minite Al4SO4(OH)10·5(H2O) over all SO4

2− concentra-tion ranges.

Nordstrom (1982) argued that in S-rich acidic envi-ronments, jurbanite would be favoured over alunitebecause slow nucleation and precipitation kinetics im-pedes alunite formation at low temperature (25 °C).However, the only Alx(SO4)y(OH)z minerals detected inthe Masaya Andosols were aluminite-like minerals Al2(SO4)(OH)4·7(H2O), for which no thermodynamic dataare available (Delfosse et al., 2005c). Further study isneeded to determine the exact chemical composition ofthe precipitated SO4

2− mineral in these soils.

The SO42− concentration in solution, which corre-

sponded to the transition between the L- and C-typeisotherms, was calculated from the intersection of tworegression equations, a Langmuir-like and a linear equa-tion at low and high concentrations, respectively. Thecalculation results indicated that the SO4

2− concentrationat which transition occurred was the lowest for the EU2-Bw sample (4.4 mM), and increased in the order EU2-BwbEU5-A2=EU9-A2 (5.4 mM)bVI2-3A (6.4 mM).This order was different from that deduced on the basis ofthe level of dissolved SO4

2− which was required to reachsaturation with respect to jurbanite (EU2-BwbEU9-A2bVI2-3AbEU5-A2). This illustrates that the satura-tion of a solution with respect to a mineral is not sufficientevidence of precipitation, an argument also developed bySposito (1984). Yet, the lowest SO4

2− concentration atwhich the abrupt slope change observed for the EU2-Bwsample may well result from the larger specific surface(Table 1) and clay content of this sample. It has beenshown that the seeding of a solution with clay enhances

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356357358359360361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390391392393394395396397398399400

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the rate of Alx(OH)y(SO4)z formation (Adams andRawajfih, 1977), highlighting the role of catalyst suchas surface area in Alx(OH)y(SO4)z formation (Nordstrom,1982).

Previous studies have considered that precipitation of aSO4

2− mineral phase would be accompanied by a decreaseinAl concentration in the solution (e.g. Rajan, 1979). Thiswas also proposed in the surface precipitation model todescribe cation sorption (Farley et al., 1985). In thismodel, the maximum of sorption through precipitationmechanism is dictated by the limited supply of the ac-companying ion (Al in this case). In the present study, thelow pH value (4), which was maintained during the ex-periment through a continuous H+ input, allowed Al to bereplenished in solution (Table 2).

The progressive, rather than sudden, removal of SO42−

from solution, i.e. the small rather than infinite slope ofthe isotherm (Fig. 1), at high SO4

2− concentrationsupports the idea that adsorption followed by surfaceprecipitation, rather than direct precipitation in solution,is the likely formation pathway of Alx(OH)y(SO4)zminerals in the S-impacted Andosols (Delfosse et al.,2005c). If SO4

2− was involved in the formation of aprecipitate in the bulk solution, its concentration wouldbe fixed by the solubility product of the precipitate. Inthis case, at constant pH and Al concentration, the slopeof the isotherm would be infinite.

In theMasaya area, SO42− concentration in soil solution

maywell be in the range needed for precipitation. Johnsonand Parnell (1986) observed a 100-fold increase betweenSO4

2− concentration inMasaya rainwater (4–9 μmol SO42−

l−1) and in soil solution (0.6 mmol SO42− l−1). Recently,

Delmelle et al. (2003) measured 51–90 μmol SO42− l−1 in

samples of rainwater collected downwind of the volcano.These concentrations are likely to generate high SO4

2−

concentrations in soil solution.

4. Conclusion

Our results have highlighted the biphasic nature ofSO4

2− sorption isotherms obtained for the Vitric andEutric Andosols from the Masaya region. Sorption ofSO4

2− corresponded to L-type and C-type isotherms atlow and high SO4

2− solution concentrations, respectively.The transition between the two curves occurred between∼5 to ∼6 mM SO4

2− in solution. The biphasic shape ofthe isotherm probably reflects a continuum between twosorption processes: adsorption in the low concentrationrange, and surface precipitation in the higher concentra-tion range. The latter process is understood in terms ofthe formation pathway of Alx(OH)y(SO4)z minerals insoils.

Acknowledgements

T. Delfosse acknowledges the financial support fromthe Belgian Fonds pour la Formation à la Recherche dansl'Industrie et l'Agriculture (FRIA). This research wassupported by the Fonds Spécial deRecherche (FSR) of theUniversité catholique de Louvain. We thank Anne Ise-rentant and Claudine Givron for the analytical assistance.We are also grateful to the anonymous reviewers for theirconstructive comments on a previous version of thismanuscript.

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