Electronic Journal of Polish Agricultural Universities (EJPAU) founded by all Polish Agriculture Universities presents original papers and review articles relevant to all aspects of agricultural sciences. It is target for persons working both in science and industry,regulatory agencies or teaching in agricultural sector. Covered by IFIS Publishing (Food Science and Technology Abstracts), ELSEVIER Science - Food Science and Technology Program, CAS USA (Chemical Abstracts), CABI Publishing UK and ALPSP (Association of Learned and Professional Society Publisher - full membership). Presented in the Master List of Thomson ISI.
Volume 5
Issue 2
Environmental Development
Available Online: http://www.ejpau.media.pl/volume5/issue2/environment/art-03.html


Jean Bernard Diatta



An attempt to evaluate adsorption parameters and charge-based densities for Pb is reported in the paper. The method was based on the calculation of Langmuir adsorption maximum (amax), and the bonding energy term (b). The parameters were the outcome of well-established linear relationships of Ce/S versus Ce (Ce, equilibrium concentration and S, amount adsorbed). The use of charge-based sorption density parameter (SDCEC), which expressed the number of accessible charges for Pb adsorption, evidenced the occurrence of two main adsorption phases, characterised by two different slopes. The first ones, varying from 0.536 to 3.144 were suggested to be attributed to ‘high attractive sites’, whereas the second with slopes from 0.011 to 0.259, probably represented ‘low attractive sites’. Charge-based sorption density parameters elucidated more Pb adsorption behaviour than did Langmuir adsorption maximum (a

Key words: Lead, adsorption parameters, Langmuir isotherm, charge density.


The reaction of metal ions with soil body depends both on the physical and chemical nature of the adsorbing surface and properties of metals. Several studies have been conducted to assess quantitatively and qualitatively the phenomena occurring at the interface aqueous-solid soil phase [2, 3, 4, 5, 8, 15]. Widely reported in the literature procedures for calculating basic sorption parameters, i.e. adsorption maximum, bonding energy term, and others, are quite frequently complex and time-consuming. Simple ways for routine and even prediction studies in order to evaluate soils potential buffering capacities for metals adsorption are quite inexistent. Therefore, it seems reasonable and helpful to present such an approach.

The aim of the current paper was to outline a simple method for evaluating Langmuir adsorption maximum, bonding energy term and a charge-based sorption density for Pb adsorption of some selected soils.


Theory outline

The Langmuir equation based on the kinetic theory of gases is extensively used to describe gas adsorption on solids. The same equation often applies to the adsorption of liquids and ions from solutions by solids although the same rigorous, theoretical basis is not as fully developed. As applied to liquids or ions, the following equation is used herein:


S - amounts of Pb adsorbed (mmolc·kg-1),
amax - adsorption maximum (mmolc·kg-1),
b - parameter related to the bonding energy of the adsorbent for the adsorbate (dm3·mmolc-1),
Ce - equilibrium Pb concentration (mmolc·dm-3).

The amount of Pb adsorbed by the soils may be calculated by:


Ci – initial Pb concentration (mmolc · dm-3)
V - volume of the initial solution, dm3,
W - weight of a soil sample, kg,
CV - correction value (amount of Pb extracted by DTPA), (mmolc·kg-1),

In its linear form, equation (1) may be rewritten as follows:


the slope is equal to and the intercept (when Ce tends closely to 0) is expressed by . The value of the bonding energy term (b) is then calculated from the ratio of the slope and the intercept, and it is equal to . It is noteworthy that the calculation of the adsorption maximum (amax) can involve errors of 50% and more [7] if the isotherm does not have correct Langmuir shape.

Soil analyses and equilibration studies

Four surface soils, namely S1, S2, S3 and S4 (Table 1) were randomly collected from arable areas (20 cm depth). The soil particle size was determined by the Prósiñski areometric method and textural soil class was established according to Soil Survey Division Staff procedure [19]; organic carbon by the method of Tiurin [12] and soil pH in 0.01M CaCl2 suspension [14]. Cation exchange capacity (CEC) was determined by a modified Mehlich8.2 method [10]. The specific surface area was determined by equilibrating soil samples with ethylene glycol monoethyl ether (EGME) according to Carter et al., [1]. The total and organically bound Pb contents were extracted in aqua regia [17] and DTPA [11], respectively.

Table 1. Some physical and chemical properties of the soils

Soil textural class

Particle size (mm)
0.1 - 0.02    < 0.02


Organic carbon





Loamy sanda (S1)









Sandy loam (S2)









Loamy sandb (S3)









Loam (S4)









a, b: for differentiation; c: Specific surface area; *: not detected; z: Exchangeable Acidity.

Equilibration studies were carried out at 20°C with applied Pb concentrations varying from 0.2 to 2.0 mmolc·dm-3 as Pb(NO3)2 in 0.01M Ca(NO3)2 (background electrolyte). Such a wide range of concentrations of metals was used to cover heterogeneity of soil samples; different duplicated soil/solution ratios of 1/15; 0.3/15; 0.2/15 and 0.15/15 were applied for soils S1; S2; S3 and S4, respectively. The slurries were agitated for 2 hours and equilibrated for 22 hours. Equilibrium concentrations (Ce) as well as total and DTPA extractable Pb were determined by AAS method (Atomic Absorption Spectrophotometry, Varian Spectra 250 plus). The soil solid-phase Pb was calculated as the difference between initial Pb concentrations (Ci) and those in solutions after equilibration. Statgraphics and Computations and illustrations were made by using Statgraphics and Excel packages.


Soil samples used in the study differed significantly in their physical and chemical properties (Table 1). For convenience the loamy sanda, sandy loam, loamy sandb and loam soils will be referred to as S1, S2, S3 and S4, respectively. Cation exchange capacity (CEC) varied from 5.97 to 21.29 cmolc·kg-1 with soils representing mostly neutral to basic reaction, except the acidic soil S1 (pH 5.00). Total lead content of the soils showed a moderate contamination level (0.79 mmolc·kg-1 or higher) according to IUNG, [9] except for the soil S3 for with Pb content amounting for 0.18 mmolc·kg-1 (Table 2).

Table 2. Total and DTPA lead content of the soils (mmolc·kg-1)

Soil textural class

Total Pb


Labile Pb* (%)

Loamy sanda (S1)




Sandy loam (S2)




Loamy sandb (S3)




Loam (S4)




*: quotient of DTPA-Pb to Total-Pb multiplied by 100.

a. Graphical evaluation of Pb sorption parameters

Metal-ion binding by natural particles is expected to be a highly nonlinear process and should therefore be dependent on the absolute concentrations of a given metal in the surrounding solution. Lead affinity to soil solid-phase surfaces was found to be notably different depending on several factors such as metal properties. The values of adsorption maxima and bonding energy terms for Pb are reported in Table 3. As it could be observed, the calculation of these parameters was facilitated by the graphical presentation of the plots of Ce/S (i.e. equilibrium to adsorbed Pb) versus Ce (equilibrium Pb) typical for the Langmuir isotherm (Fig. 1, Fig. 2, Fig. 3 and Fig. 4). The resulting straight lines were the requisite conditions for calculating the adsorption maximum (amax) and the bonding energy term (b) that derived from the slopes and intercepts, respectively, as reported in Equ. 3. This is important, since serious deviation from linearity may generate results burdened with 50% errors, or even higher as reported by Harter [7]. The soil solid-phase formation of Pb may be strictly related to its chemistry on one hand and the soil medium, on the other. If we restrict soil properties to organic matter, clay and carbonates content, reflecting the relative magnitude of soils buffering properties expressed by their CEC, then the values of amax, b and MBC seem to prove geochemical specificity of Pb adsorption by soils. According to Santillan-Medrano and Jurinak [16] lead reaction in slightly calcareous soils is very effective with a resultant of mixed compounds such as PbCO3, Pb(OH)2, typical for chemisorption. It seems consistent with the following order expressing the relative degree of CEC saturation (amax/CEC):

105% (S3) > 100% (S4) > 73% (S2) > 30% (S1)

Table 3. Adsorption parameters calculated from the plots of Ce/S versus Ce for Pb of the Soils.

Soil textural class







Loamy sanda (S1)



17.73* ± 0.76

8.94 ± 0.38

158.50 ± 6.79


Sandy loam (S2)



96.15 ± 16.05

94.54 ± 15.13

9090.02 ± 1569.35


Loamy sandb



161.29 ± 46.71

41.33 ± 7.67

6666.12 ± 1448.01


Loam (S4)



212.76 ± 64.96

16.20 ± 4.33

3446.71 ± 1017.97


x: adsorption maximum; y: bonding energy term; z: maximal buffering capacity (amax · b).
*: mean values and standard deviation; R2: coefficient of determination.
More details see "Materials and Methods" and Figs. 1.

Figure 1. Langmuir isotherm for Pb adsorption by the soil S1

Figure 2. Langmuir isotherm for Pb adsorption by the soil S2

Figure 3. Langmuir isotherm for Pb adsorption by the soil S3

Figure 4. Langmuir isotherm for Pb adsorption by the soil S4

Oversaturation of CEC in soil S3 most likely originated from occurrence of carbonates, which in turn led both to Pb adsorption and precipitation resulting in formation of stable soil complexes, as reported by Sposito et al. [20] and Elkhatib et al. [4]. The suggested method to evaluate adsorption maximum (amax) gave reliable results irrespective of soil types. The magnitude of amax values was found to conform the order observed for the specific surface area, (SSA) and the cation exchange capacity, (CEC).

b. Lead sorption densities approach

Sorption processes, especially nonspecific adsorption, are greatly influenced by the surface charge of which cation exchange capacity (CEC) is a measure. Amounts of lead adsorbed in the CEC may be expressed as ions per moles of charge, including thus a charge-based sorption characteristics. Such charge-based sorption density, SDCEC as suggested by Schulte and Beese [18] and Zehetner and Wenzel [24], was adapted for Pb as follows:


SDCEC - charge-based sorption density, (ions·molc-1),
NA - Avogadro's number, (6.023 x 1023 ions·molc-1).

The relationships between Pb solution concentrations and their corresponding charge-based sorption densities presented in Fig. 5, Fig. 6, Fig. 7 and Fig. 8, suggest the use of the sorption densities as a mean of evaluating quantity-intensity relationships of Pb in soils. Affinity of Pb towards negatively charged CEC-sites may be assessed with satisfactory accuracy. For example, at equilibrium concentration, Ce of 5.0 µmolc·dm-3 the charge-based sorption densities (SDCEC) for Pb will amount to 1.6 x 1022; 20.3 x 1022; 15.1 x 1022 and 0.52 x 1022 ions·molc-1 for soils S1; S2; S3 and S4, respectively. SDCEC of soils S2 and S4 deserve additional consideration due to inflection of the lines. Proper i nflection points represented equilibrium concentrations of Ce = 4.07 and 16.98 µmolc·dm-3 corresponding to SDCEC of 16.79 x 1022 and 24.49 1022 ions·molc-1 for soils S2 and S4, respectively. With further additions of Pb behind the inflexion point, the increase of SDCEC values was relatively low in comparison with the ones recorded for Pb levels up to the inflection point. Such slight increase of SDCEC may be attributed to the occurrence of new population of sorbing sites characterized by weak attraction energies. This is consistent with the findings of Msaky and Calvet, [13]; Basta and Tabatabai, [2] who reported high affinity of soils for copper at low concentration, which decreased with further increase of concentration.

Figure 5. Isotherms of the sorption density (SDCEC) vs equilibrium concentration (Ce) for the soil S1

Figure 6. Isotherms of the sorption density (SDCEC) vs equilibrium concentration (Ce) for the soil S2

Figure 7. Isotherms of the sorption density (SDCEC) vs equilibrium concentration (Ce) for the soil S3

Figure 8. Isotherms of the sorption density (SDCEC) vs equilibrium concentration (Ce) for the soil S4

Furthermore, it is noteworthy to point out the L-type linear shapes [6; 22] of Pb charge-based sorption density isotherms of the soils. The Langmuir one-site isotherm is conceptually valid for monolayer sorption on a surface containing a finite number of binding sites. Moreover, the treatment assumes uniform energies of sorption on the surface and no transmigration of adsorbates into the plane of the surface. Such restrictions are not applicable to solids characterised by heterogeneous adsorptive surface like those found in soil systems. Data analysis and interpretation based solely on Langmuir adsorption maximum (amax) should be undertaken with care since it does not outline some sorption particularities as illustrated in Fig. 5, Fig. 6, Fig. 7 and Fig. 8. Interestingly, SDCEC values did not follow the order observed both for the specific surface area (SSA) and cation e xchange capacity (CEC) as listed in Table 1. Lead was adsorbed basically at two types of sites represented by two straight lines: the first is indicative of energetically high sites with a relatively high slope, whereas low energetic sites appeared in the second range being characterized by a decreasing slope. Therefore, the isotherms are in agreement with occurrence of heterogeneous adsorption surface which consisted of adsorption sites of high and low energy [20; 23]. On the basis of the slopes, the soils may be ranked as follows:

High energetic sites:

S4 (slope = 3.14) > S2 (0.93) > S3 (0.79) > S1 (0.54)

Low energetic sites:

S2 (slope = 0.26) > S3 (0.21) > S1 (0.16) > S4 (0.011)

The observed ranks, both for high and low charge distribution showed that the sorptive complex of investigated soils can not be restricted to a single adsorption parameter. Furthermore, as clearly evidenced by relationships between SDCEC and Pb equilibrium concentration, Pb adsorption expressed in terms of charge-based density could be used as a simple and efficient parameter for accurate evaluation of soil capacity for Pb adsorption. The approach may be of practical use also for ecotoxicology assessment.


  1. Well-defined linear relationships between Ce/S and Ce are prerequisite conditions for Langmuir adsorption parameters (amax and b) calculation.

  2. Occurrence of carbonates may enhance Pb adsorption leading thus to an “oversaturation” of the sorptive complex as a result of chemisorption.

  3. Expressing lead adsorption in terms of charge-based sorption density allowed deeper insight into the adsorption process than offered by Langmuir adsorption maximum approach.

  4. All investigated soils were characterized by a two-phase adsorption process. The mechanisms involved stressed evidence of both high and low adsorption sites.

  5. Evaluation of adsorption parameters, as outlined herein, seems to be easily applicable and may provide valuable information about adsorption processes.


  1. Carter D. L., Mortland M. M., Kemper W. D.: Specific surface. In “Methods of Soils Analysis, Part I – Physical and Mineralogical Methods” (A. Klute, ed.) 2nd ed.; pp. 413-423. Am. Soc. Agron., Madison, WI., 1986.

  2. Basta N. T., and Tabatabai M. A.: Effect of cropping systems on adsorption of metals by soils: II effect of pH. Soil Sci. 153:195-204, 1992.

  3. Diatta J. B., Kocialkowski W.: Adsorption of zinc in some selected soils. Pol. J. Environ. Stud. 7(4):195-200, 1998.

  4. Elkahatib E. A., Elshebiny G. M. Elsubruiti G. M. and M. A. Balba: Thermodynamics of lead sorption and desorption in soils. Z. Pflanzenernahr, Bodenk., 156:461-465, 1993.

  5. Gao S., Walker W. J., Dahlgren R. A., Bold J.: Simultaneous sorption of Cd, Cu, Ni, Zn, Pb, and Cr on soils treated with sewage sludge supernatant. Wat., Air and Soil Poll., 93:331-345, 1997.

  6. Giles C. H., McEwan T. H., Nakhawa S. N., and Smith D.: Studies in adsorption. Part XI. A system of classification of solution adsorption isotherms, and its use in diagnosis of adsorption mechanisms and in measurement of specific surface areas of solids. J. Chem. Soc., 3973-93, 1960.

  7. Harter R. D : Curve-fit errors in Langmuir adsorption maxima. Soil Sci. Soc. Am J., 48: 749-752, 1984.

  8. Helios-Rybicka E., Calmano W. and Breeger A: Heavy metals sorption/desorption on competing clay minerals; an experimental study. Appl. Clay Sci., 9:369-381, 1995.

  9. IUNG: Assessment of degree of heavy metals and sulphur contamination in soils and plants [Ocena stopnia zanieczyszczenia gleb i roslin metalami ciezkimi i siarka]. Pulawy, p. 20, 1993.

  10. Kocialkowski W. Z., Ratajczak M. J.: A simplified Mehlich method for determining exchangeable cations and cation exchange capacity of soils [Uproszczona metoda oznaczania kationow wymiennych oraz pojemnosci wymiennej w stosunku do kationow gleby wedlug Mehlicha]. Rocz. AR- Poznañ; CXLVI, 106-116, 1984.

  11. Lindsay W. L., and Norvell W. A.: Development of a DTPA soil test for zinc, iron, manganese and copper. Soil Sci. Soc. Am. J., 42:421-428, 1978.

  12. Litynski T. Jurkowska H., and Gorlach E.: Agrochemical analysis. Methodical guide for soils and fertilizers’ analysis [Analiza chemiczno-rolnicza. Przewodnik metodyczny do analizy gleb i nawozow. PWN, Warszawa]. PWN, Warszawa, 1976.

  13. Msaky J. J. and Calvet R. (1990): Adsorption behaviour of copper and zinc in soils: Influence of pH on adsorption characteristics. Soil Sci., 150(2):513-522.

  14. Polish Standard: Polish Standarisation Committee, ref. PrPN-ISO 10390 (E), Soil quality and pH determination [Jakosc gleby i oznaczanie pH]. First edition [Pierwsze wydanie], 1994.

  15. Salim I. A., Miller C. J., Howard J. J.: Sorption isotherm-sequential extraction analysis of heavy metal retention in landfill liners. Soil Sci. Soc. Am. J., 60:107-114, 1996.

  16. Santillan-Medrano J. and Jurinak J. J.: The chemistry of lead and cadmium in soil: solid phase formation. Soil Sci. Soc. Am. Proc., 39:851-856, 1975.

  17. Sauerbeck D., Lubben S.: Okologie ein Forderschwerpunkt des BMFT, band 6/1991. ISBN 3-89336 - 081 – 6, 1991.

  18. Schulte A. and Beese F.: Isotherms of cadmium sorption density. J. Environ. Qual. 712-718, 1994.

  19. Soil Survey Division Staff: Soil Survey Manual. USDA, Handbook Np. 18, 1994.

  20. Soko³owska Z. (1989): Role of surface heterogeneity on adsorption processes in soils [Rola niejednorodnosci powierzchni w procesach adsorpcji zachodzacych na glebach.] Agrophysical Issues [Problemy Agrofizyki], 58:1-170.

  21. Sposito G., Holtzclaw K. M. and LeVesque-Madore C. S.: Cupric ion complexation by fulvic acid extracted from sewage sludge-soil mixtures Soil Sci. Soc. Am. J. 43, 1148-1155, 1979.

  22. Sposito G.: The surface chemistry of soils. Oxford Univ. Press. New York, 1984.

  23. Wu J., Laird D. A. and Thompson M. L. (1999): Sorption and desorption of copper on soil clay components. J. Environ. Qual. 29(1):334-338.

  24. Zehetner F. and Wenzel W.W.: Nickel and copper sorption in acid forest soils. Soil Sci. 165 (6):463-472, 2000.

Jean Bernard Diatta
Department of Agricultural Chemistry
Wojska Polskiego 71F, 60-625 Poznañ
Tel. +48618487783, Fax: +48618487787
e-mail: Jeandiatta@yahoo.com

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