Skip to main content
SpringerLink
Log in

Mathematical modeling and interpretation of equilibrium isotherms of Pb (II) from aqueous media by Chlorella pyrenoidosa immobilized in Luffa cylindrica

  • Original Article
  • Published:
Biomass Conversion and Biorefinery Aims and scope Submit manuscript

Abstract

New sorbent was prepared from unicellular green microalgal Chlorella pyrenoidosa (CP) immobilized in Luffa cylindrica (CP-LC) as a biosorbent for the removal of lead ions from aqueous media in a batch experiment mode. The prepared biosorbent was characterized by Fourier transform infrared spectroscopy (FTIR) and scanning electron microscopy (SEM). In the experimental design of the Pb (II) removal process, the equilibrium isotherms were studied and modeled. To select the best-fit isotherm model for this biological process, the experimental data were fitted in the eighteen different types of one-, two-, three-, four-, and five-parameter isotherm models. A comparison of non-linear models for selecting the optimum isotherm showed Fritz–Schlunder (V) model gives the most accurate fit to describe the experimental data, determined based on several error functions. Taking into account the outcome and in an attempt to optimize the equilibrium isotherms, the equation of Fritz-Schlünder (V) was modified to obtain more sophisticated model and more precision parameters values. As a consequence of such a developed model to existing mentioned ones, the mathematical model developed in this study is more suitable for predicting the equilibrium data. According to the results obtained, the evaluation of experimental data in terms of biosorption kinetics elucidated that the biosorption of Pb (II) by CP-LC well followed pseudo-second-order kinetics. The maximum biosorbent capacity of CP-LC was found to be 123 mg/g for 40 min at pH5. The calculated thermodynamic factors (∆G°, ∆H°, and ∆S°) indicated that the biosorption process was favorable, spontaneous, and exothermic at 298–318 K.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Abbreviations

Ak (mg/g):

Koble-Carrigan isotherm constant

ae (-):

Activity of Pb (II) in solution at equilibrium

akh (–):

Constant in Khan isotherm

aR (L/g):

Constant in Redlich–Peterson isotherm

ARE:

average relative error

A T (L/g):

Equilibrium binding constant

as:

Activity of adsorbed Pb (II)

bo (L/g):

Constant in Baudu isotherm

Bk (L/g):

Koble-Carrigan isotherm constant

bKH (L/g):

Constant in Khan isotherm

bR (–):

Constant in Redlich–Peterson isotherm

BT (Kj/mol):

Temkin constant

b T (Kj/mol):

Adsorption energy

C (L/g):

Fritz-Schlünder (IV) constant

C0 (mg/L):

Initial Pb (II) ion concentration

Ce (mg/L):

Pb (II) ion concentration in solution at equilibrium

Cs (mg/g):

Pb (II) adsorbed on CP-LC

CP:

Chlorella pyrenoidosa

CP-LC:

Chlorella pyrenoidosa immobilized in luffa cylindrica

D (L/g):

Fritz-Schlünder (IV) constant

ERSQ (–):

Sum of the squares of the errors

GM:

Growth medium

HYBRID:

Hybrid fractional error function

IUPAC:

International union of pure and applied chemistry

K (–):

Henry’s isotherm model adsorption constant

K1 (1/min):

The rate constant of pseudo first-order model

K2 (g/mg/min):

the rate constant of pseudo second-order model

Kc (-):

The distribution constant

K K1 (L/g):

Kiselev equilibrium constant

K K2 (–):

Constant of complex formation between adsorbed molecules

KE (L/mg):

Elovich constant

K F (mg/g)(L/g)1/n :

Adsorption capacity

K FH (L/g):

Flory–Huggins equilibrium constant

K FG (L/g):

Fowler–Guggenheim equilibrium constant

KFS1 (L/g):

Fritz-Schlünder (v) equilibrium constant

kFS2 (L/g):

Fritz-Schlünder (v) equilibrium constant

K H (L/g):

Hill–de Boer constant

KL (L/mg):

Constant in Langmuir isotherm

K n (k/J/mol):

E nergetic constant of the interaction between adsorbed molecules

KR (L/g):

Constant in Redlich–Peterson isotherm

KRP (L/g):

Constant in Radke–Prausnitz isotherm

ks (L/g):

Constant in Sips isotherm

KT (L/g):

Constant in Toth isotherm

m (g/L):

Dose of free or immobilized cells

M1, M2 (–):

Constants in Fritz-Schlünder model

MPSD:

Marquardt’s percent standard deviation

N (–):

Number of observations in the experimental isotherm

n (–):

Constant in Freundlich isotherm

n FH (–):

Number of adsorbates occupying adsorption sites

nK (–):

Noefficient in Koble-Carrigan isotherm

nR (–):

Constant in Radke–Prausnitz isotherm

nS (–):

Coefficient in Sips isotherm

nT (–):

Constant in Toth isotherm

P (–):

Number of parameters in the regression model

qcal (mg/g):

Estimate from the isotherm for corresponding qexp

qe (mg/g):

Adsorption capacity

qexp (mg/g):

Observation from the batch experiment

q mKH (mg/g):

Maximum adsorbate uptake from Khan model

q m (mg/g):

Maximum adsorbate uptake from Radke–Prausnitz model

q mb (mg/g):

Maximum adsorbate uptake from Baudu model

q max (mg/g):

Maximum adsorbate uptake from Langmuir model

q mE (mg/g):

Maximum adsorbate uptake from elovich model

푞mFS (mg/g):

Fritz-Schlünder (v) maximum adsorption capacity.

q mk (mg/g):

Maximum adsorbate uptake from Toth model

q mS (mg/g):

Maximum adsorbate uptake from sips model

R (J/mol K):

Ideal gas constant

R2 (–):

Coefficient of determination

RL (-):

Separation factor

S2 :

Residual variance

SEM:

Scaninig electron microscopy

t (min):

Time

T (K):

Temperature

W (KJ/mol):

Interaction energy between adsorbed molecules

x, y (–):

Constants in Baudu isotherm

Ye (–):

Activity coefficient of Pb (II) in equilibrium solution

Ys (–):

Activity coefficient of adsorbed Pb (II)

∆H◦ (kJ/mol):

Enthalpy change

∆S◦ (J/mol K):

Entropy change

∆G◦(kJ/mol):

Gibbs free energy change (kJ/mol)

Ø (–):

Surface coverage of the adsorbent

α, ß (–):

Constant in modified Fritz-Schlunder (v)

References

  1. Wei BG, Yang LS (2010) A review of heavy metal contaminations in urban soils, urban road dusts and agricultural soils from China. Microchem J 94:99–107. https://doi.org/10.1016/j.microc.2009.09.014

    Article  Google Scholar 

  2. Wang J, Chen C (2006) Biosorption of heavy metals by Saccharomyces cerevisiae: a review. Biotechnol Adv 24(5):427–451. https://doi.org/10.1016/j.biotechadv.2006.03.001

    Article  Google Scholar 

  3. Abhari PS, Manteghi F, Tehrani Z (2020) Adsorption of lead ions by a green AC/HKUST-1 nanocomposite. Nanomaterials 10(9):1647. https://doi.org/10.3390/nano10091647

    Article  Google Scholar 

  4. Agarwal A, Upadhyay U, Sreedhar I, Singh SA, Patel CM (2020) A review on valorization of biomass in heavy metal removal from wastewater. J Water Process Eng 38:101602. https://doi.org/10.1016/j.jwpe.2020.101602

    Article  Google Scholar 

  5. Moreira VR, Lebron YAR, Freire SJ, Santos LVS, Palladino F, Jacob RS (2019) Biosorption of copper ions from aqueous solution using Chlorella pyrenoidosa: optimization, equilibrium and kinetics studies. Microchem J 145:119–129. https://doi.org/10.1016/j.microc.2018.10.027

    Article  Google Scholar 

  6. Vidal CB, Melo DQ, Raulino GSC, da Luz AD, da Luz C, Nascimento RF (2016) Multielement adsorption of metal ions using Tururi fibers (Manicaria saccifera): experiments, mathematical modeling and numerical simulation. Desalin Water Treat 57(19):9001–9008. https://doi.org/10.1080/19443994.2015.1025441

    Article  Google Scholar 

  7. Kumar KV (2006) Comparative analysis of linear and non-linear method of estimating the sorption isotherm parameters for malachite green onto activated carbon. J Hazard Mater 136(21):197–202. https://doi.org/10.1016/j.jhazmat.2005.09.018

    Article  Google Scholar 

  8. Kumar KV, Porkodi K (2006) Relation between some two- and three-parameter isotherm models for the sorption of methylene blue onto lemon peel. J Hazard Mater 138:633–635

    Article  Google Scholar 

  9. Haloi N, Sarma HP, Chakravarty P (2013) Biosorption of lead (II) from water using heartwood charcoal of Areca catechu: equilibrium and kinetics studies. Appl Water Sci 3:559–565. https://doi.org/10.1007/s13201-013-0112-3

    Article  Google Scholar 

  10. Kuczajowska-Zadrożna M, Filipkowska U, Jóźwiak T (2020) Adsorption of Cu (II) and Cd (II) from aqueous solutions by chitosan immobilized in alginate beads. J Environ Chem Eng 8:103878. https://doi.org/10.1016/j.jece.2020.103878

    Article  Google Scholar 

  11. Al-Ghouti MA, Da'ana DA (2020) Guidelines for the use and interpretation of adsorption isotherm models: a review. J Hazard Mater 393:122383. https://doi.org/10.1016/j.jhazmat.2020.122383

    Article  Google Scholar 

  12. Rangabhashiyam S, Anu N, Giri Nandagopal MS, Selvaraju N (2014) Relevance of isotherm models in biosorption of pollutants by agricultural byproducts. J Environ Chem Eng 2(1):398–414. https://doi.org/10.1016/j.jece.2014.01.014

    Article  Google Scholar 

  13. Bayuo J, Abukari MA, Pelig-Ba KB (2020) Desorption of chromium (VI) and lead (II) ions and regeneration of the exhausted adsorbent. Appl Water Sci 10:171. https://doi.org/10.1007/s13201-020-01250-y

    Article  Google Scholar 

  14. Ding TY, Hii SL, Ong, L (2012) Ong, Comparison of pretreatment strategies for conversion of coconut husk fiber to fermentable sugars. Bioresources 7(2): 1540–1547. https://doi.org/10.15376/biores.7.2.1540-1547.

  15. Rescignano N, Fortunati E, Armentano I, Hernandez R, Mijangos C, Pasquino R, Kenny JM (2015) Use of alginate, chitosan and cellulose nanocrystals as emulsion stabilizers in the synthesis of biodegradable polymeric nanoparticles. J Colloid Interface Sci 445:31–39. https://doi.org/10.1016/j.jcis.2014.12.032

    Article  Google Scholar 

  16. Mitra T, Sailakshmi G, Gnanamani A, Mandal AB (2013) Studies on cross-linking of succinic acid with chitosan/collagen. Mater Res 16:755–765. https://doi.org/10.1590/S1516-14392013005000059

    Article  Google Scholar 

  17. Lim SH, Hudson SM (2004) Synthesis and antimicrobial activity of a water-soluble chitosan derivative with a fiber-reactive group. Carbohydr Res 339:313–319. https://doi.org/10.1016/j.carres.2003.10.024

    Article  Google Scholar 

  18. Bhattacharya A, Mathur M, Kumar P, Malik A (2019) Potential role of N-acetyl glucosamine in Aspergillus fumigatus-assisted Chlorella pyrenoidosa harvesting. Biotechnol Biofuels 12:178. https://doi.org/10.1186/s13068-019-1519-3

    Article  Google Scholar 

  19. Leal D, Matsuhiro B, Rossi M, Caruso F (2008) FT-IR spectra of alginic acid block fractions in three species of brown seaweeds. Carbohydr. Res, 343(2): 308-316. https://doi.org/10.1016/j.carres.2007.10.016.

  20. Taşar Ş, Kaya F, Özer A (2014) Biosorption of lead(II) ions from aqueous solution by peanut shells: equilibrium, thermodynamic and kinetic studies. Journal of Environmental Chemical Engineering. J Environ Chem Eng 2(2):1018–1026. https://doi.org/10.1016/j.jece.2014.03.015

    Article  Google Scholar 

  21. Ozer A (2007) Removal of Pb(II) ions from aqueous solutions by sulphuric acid-treated wheat bran. J Hazard Mater 141(3):753–761. https://doi.org/10.1016/j.jhazmat.2006.07.040

    Article  Google Scholar 

  22. Adewuyi A, Pereira FV (2017) Underutilized Luffa cylindrica sponge: a local bio-adsorbent for the removal of Pb(II) pollutant from water system. Beni Suef Univ J Basic Appl Sci 6(2):118–126. https://doi.org/10.1016/j.bjbas.​2017.02.001

    Article  Google Scholar 

  23. Karnib M, Kabbani A, Holail H, Olama,Z (2014) Heavy metals removal using activated carbon, silica and silica activated carbon composite. Energy Procedia 50: 113–120. doi: https://doi.org/10.1016/j.egypro.2014.06.014.

  24. Ajenifuja E, Ajao JA, Ajayi EOB (2017) Adsorption isotherm studies of Cu (II) and Co (II) in high concentration aqueous solutions on photocatalytically modified diatomaceous ceramic adsorbents. Appl Water Sci 7:3793–3801. https://doi.org/10.1007/s13201

    Article  Google Scholar 

  25. Awwad A M, Salem N M (2014) Kinetics and thermodynamics of Cd(II) biosorption onto loquat (Eriobotrya japonica) leaves. J Saudi Chem Soc 18 (5): 486–493. https://doi.org/10.1016/j.jscs.2011.10.007.

  26. Bhaumik R, Mondal NK (2016) Optimizing adsorption of fluoride from water by modified banana peel dust using response surface modelling approach. Appl Water Sci 6:115–135. https://doi.org/10.1007/s13201-014-0211-9

    Article  Google Scholar 

  27. Farhan SN, Khadom AA (2015) Biosorption of heavy metals from aqueous solutions by Saccharomyces Cerevisiae. Int J Ind Chem 6(2):119–130. https://doi.org/10.1007/s40090-015-0038-8

    Article  Google Scholar 

  28. Wei W, Wang Q, Li A, Yang J, Ma F, Pi S, Wu D (2016) Biosorption of Pb (II) from aqueous solution by extracellular polymeric substances extracted from Klebsiella sp. J1: adsorption behavior and mechanism assessment. Sci Rep 6:31575. https://doi.org/10.1038/srep31575

    Article  Google Scholar 

  29. Zulkali MMD, Ahmad AI, Norulakmal NH, Sharifah NS (2006) Comparative studies of Oryza sativa L. husk and chitosan as lead adsorbent. J Chem Technol Biotechnol 81:1324–1327. https://doi.org/10.1002/jctb.1429

    Article  Google Scholar 

  30. Sarı A, Tuzen M, Uluözlü ÖD, Soylak M (2007) Biosorption of Pb(II) and Ni(II) from aqueous solution by lichen (Cladonia furcata) biomass. Biochem Eng J 37(2):151–158. https://doi.org/10.1016/j.bej.2007.04.007

    Article  Google Scholar 

  31. Ronda A, Martín-Lara MA, Dionisio E, Blázquez G, Calero M (2013) Effect of lead in biosorption of copper by almond shell. J Taiwan Inst Chem Eng 44(3):466–473. https://doi.org/10.1016/j.jtice.2012.12.019

    Article  Google Scholar 

  32. Mahamadi C, Nharingo T (2010) Competitive adsorption of Pb2+, Cd2+ and Zn2+ ions onto Eichhornia crassipes in binary and ternary systems. Bioresour Technol 101(3):859–864. https://doi.org/10.1016/j.biortech.2009.08.097

    Article  Google Scholar 

  33. Gundogdu A, Ozdes D, Duran C, Bulut VN, Soylak M, Senturk HB (2009) Biosorption of Pb(II) ions from aqueous solution by pine bark (Pinus brutia Ten.). Chem Eng Sci 153(1-3):62–69. https://doi.org/10.1016/j.cej.2009.06.017

    Article  Google Scholar 

  34. Naiya TK, Bhattacharya AK, Das SK (2008) Adsorption of Pb(II) by sawdust and neem bark from aqueous solutions. Environ Prog 27(3):313–328. https://doi.org/10.1002/ep.10280

    Article  Google Scholar 

  35. Pavan FA, Mazzocato AC, Jacques RA, Dias SLP (2008) Ponkan peel: a potential biosorbent for removal of Pb(II) ions from aqueous solution. "Biochem. Eng. J 40(2): 357–362. https://doi.org/10.1016/j.bej.2008.01.004.

Download references

Acknowledgements

The authors (s) thank the anonymous reviewers for helping us to present this research in a more effective manner. The authors also are thankful to Mr. Ramzi Touchan, Research Professor at the Laboratory of Tree-Ring Research, University of Arizona, for his critical suggestions.

Author information

Authors and Affiliations

  1. Department Process Engineering, Faculty of Technology, University Amar Telidji-Laghouat, B.P 37G, 03000, Laghouat, Algeria

    Imane Nouacer, Mokhtar Benalia & Mebrouk Djedid

  2. Department Process Engineering, Faculty of Technology, University Hassiba Ben Bouali Chlef, P.O Box.151, 02000, Chlef, Algeria

    Ghania Henini & Ykhlef Laidani

Authors
  1. Imane Nouacer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mokhtar Benalia
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ghania Henini
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mebrouk Djedid
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ykhlef Laidani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Imane Nouacer.

Ethics declarations

Conflict of interest

The authors declare  that they have no conflict of interest.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nouacer, I., Benalia, M., Henini, G. et al. Mathematical modeling and interpretation of equilibrium isotherms of Pb (II) from aqueous media by Chlorella pyrenoidosa immobilized in Luffa cylindrica. Biomass Conv. Bioref. 13, 7839–7858 (2023). https://doi.org/10.1007/s13399-021-01722-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13399-021-01722-4

Keywords

Search

Navigation