, Volume 21, Issue 6–7, pp 445–458 | Cite as

Chemical equilibrium of ion exchange in the binary mixture Cu2+ and Ca2+ in calcium alginate

  • M. G. C. da Silva
  • R. L. S. Canevesi
  • R. A. Welter
  • M. G. A. VieiraEmail author
  • E. A. da Silva


Biopolymer alginate is capable of triggering interchain interactions in the presence of divalent and trivalent cations. Calcium alginate particles obtained by the emulsification method have been used in ion-exchange packed bed tests to remove synthetic copper effluents. Adsorption equilibrium data were obtained from single and binary component systems, which were subsequently subject to mathematical modeling. In the case of the modeling system with binary components, where the calcium was considered as a second ion, there was no significant improvement for the models analyzed, in counterpoise to the isotherm models applied to the single component system. The ideal law of mass action and the law of mass action which presupposed that both phases were non-ideal showed similar results. This process was found to be effective and feasible for industrial applications used to in heavy metal removal processes.


Ion exchange Copper Calcium alginate Modeling 

List of symbols


Activity of the compound i in phase α


Debye Huckel constant


Freundlich constant considering the presence of copper in the binary mixture (L/meq)


Freundlich constant considering the copper and calcium binary mixture (L/meq)


Parameter associated with the bioadsorbent adsorption capacity (L/meq)


Number of empty sites


Total number of available sites


Bromley parameter involving the cation i and the anion j


Active sites connected to copper ions


Active sites connected to calcium ions


Active sites connected to copper and calcium ions


Metal solution concentration in equilibrium state (meq/L)


Available cation exchange capacity (meq/g)


Total cation exchange capacity (meq/g)


Sum of interaction parameters


Objective function


Ionic length (molal)


Thermodynamic equilibrium constant of the ion exchange reaction between copper and calcium


Parameter associated with the free energy of biosorption (mg/L)


Langmuir model competition


Langmuir competition model


Langmuir competition model


Langmuir competition model


Langmuir power and Lang–Freundlich models


Langmuir power and Lang–Freundlich models


Bed height covered by ionic solution (eq. ad. and des.) (cm)


Molality of component i (molal)


Parameter associated with the effect of the concentration of metal ions on the adsorption capacity


Freundlich constant of component i considering a binary mixture


Amount adsorbed (meq/g)


Maximum amount adsorbed (meq/g)


Amount of component i adsorbed


Ratio between the amount of adsorbed and desorbed ions of alginate particles


Time (min)


Power flow system in porous bed (mL/min)


Fraction of component i in solid phase


Bed height (equation of ratio between ad. and des.) (cm)


Ionic charge of component i


Arithmetic average between cation i and anion j



Parameter of Freundlich model for Copper ion


Parameter of Freundlich model for Calcium ion


Coefficient of fugacity


Activity coefficient of component i in phase α


Parameter fitted for each model used according to the objective function Fobj, used


Wilson parameter involving cation i and anion j



Solid phase—alginate




Solid phase—resin (alginate)


Aqueous phase—solution









Number of components


Number referring to the total test concentration


Copper fraction at a given total concentration



The authors would like to acknowledge the financial support received from FAPESP and CNPq for this research.


  1. Allen, R.M., Addison, P.A.: The characterization of binary and ternary ion exchange equilibria. Chem. Eng. J. 40, 151–158 (1989)CrossRefGoogle Scholar
  2. Bailey, J.E., Ollis, D.F.: Biochemical, p. 984. Engineering Fundamentals, McGraw-Hill, New York (1986)Google Scholar
  3. Bertagnolli, C., Uhart, A., Dupin, J.C., Da Silva, M.G.C., Guibal, E., Desbrieres, J.: Biosorption of chromium by alginate extraction products from Sargassum filipendula: Investigation of adsorption mechanisms using X-ray photoelectron spectroscopy analysis. Bioresour. Technol. 164, 264–269 (2014)CrossRefGoogle Scholar
  4. Bromley, L.A.: Thermodynamic properties of strong electrolytes in aqueous solutions. AIChE J. 19(2), 313–320 (1973)CrossRefGoogle Scholar
  5. Chen, J.P., Wang, L., Zou, S.W.: Determination of lead biosorption properties by experimental and modeling simulation study. Chem. Eng. J. 131, 209–215 (2007)CrossRefGoogle Scholar
  6. Chern, J.M., Chien, Y.W.: Adsorption isotherms of benzoic acid onto activated carbon and breakthrough curves in fixed-bed columns. Ind. Eng. Chem. Res. 40, 3775–3780 (2001)CrossRefGoogle Scholar
  7. Chong, K.H., Volesky, B.: Description of two-metal biosorption equilibria by Langmuir type Models. Biotechnol. Bioeng. 47, 451–460 (1995)CrossRefGoogle Scholar
  8. Cooney, D.O.: Adsorption design for wastewater treatment. Lewis Publisher, Boca Raton (1999)Google Scholar
  9. Davis, T.A., Volesky, B., Mucci, A.: A review of the biochemistry of heavy metal biosorption by brown algae. Water Res. 37, 4311–4330 (2003)CrossRefGoogle Scholar
  10. Díaz, E.D.A., Velasco, M.C.V., Pérez, F.R., López, C.A.R., Ibarreta, L.L.: Utilización de adsorbentes baseados en Quitosano y Alginático Sódico para la eliminación de iones metálicos: Cu2+, Pb2+, Cr2+y Co2+. Rev. Iberoam. de Polym. 8(1), 20–37 (2007). (in Spanish) Google Scholar
  11. Fundueanu, G., Nastruzzi, C., Carpov, A., Desbrieres, J., Rinauto, M.: Physico-chemical characterization of Ca-alginate microparticles produced with different methods. Biomaterials 20, 1427–1435 (1999)CrossRefGoogle Scholar
  12. Hindarso, H., Ismadji, S., Wicaksana, F., Indraswati, N., Mudjijati, : Adsorption of benzene and toluene from aqueous solution onto granular activated carbon. J. Chem. Eng. Data 46, 788–791 (2001)CrossRefGoogle Scholar
  13. Jain, J.S., Snoeyink, V.L.: Adsorption from biosolute systems on active carbon. J. Water Pollut. Control Fed. 45, 2463–2479 (1973)Google Scholar
  14. Klein, G., Tondeur, D.: Multicomponent ion exchange in fixed beds. Ind. Eng. Chem. Fundam. 6(3), 39–351 (1967)Google Scholar
  15. Kleinübing, S.J.: Bioadsorção competitiva dos íons níquel e cobre em alginato e alga marinha Sargassum filipendula. Doctoral Thesis. School of Chemical Engineering – UNICAMP, Campinas-SP (2009) (in Portuguese)Google Scholar
  16. Ko, D.C.K., Porter, J.F., Mckay, G.: Film-pore diffusion model for the fixed bed sorption of copper and cadmium ions onto bone char. Water Res. 35, 3876–3886 (2001)CrossRefGoogle Scholar
  17. Kummert, R., Stumm, W.: The surface complexation of organic-acids on hydrous gamma-Al2O3. Colloid Interface Sci. 75, 373–385 (1980)CrossRefGoogle Scholar
  18. Lai, Y.L., Annaduarai, G., Huang, F.C., Lee, J.F.: Biosorption of Zn (II) on the different Ca-alginate beads from aqueous solution. Bioresour. Technol. 99, 6480–6487 (2008)CrossRefGoogle Scholar
  19. Lee, I.H., Kuan, Y.C., Chern, J.M.: Equilibrium and kinetics of heavy metal ion exchange. J. Chin. Inst. Chem. Eng. 38, 71–84 (2006)CrossRefGoogle Scholar
  20. Lima, L.K.S., Pelosi, B.T., Kleinübing, S.J., Silva, M.G.C., Vieira, M.G.A.: Avaliação da remoção de íons metálicos utilizando a macrófita aquática Salvinia natans. Proceedings of XXXV Congresso Brasileiro de Sistemas Particulados. São Carlos-SP, Cubo, 1, pp. 145–152 (2012) (in Portuguese)Google Scholar
  21. Limons, R. S.: Avaliação do potencial de utilização da macrófita aquática seca Salvinia sp. no tratamento de efluentes de fecularia. Master Thesis, School of Chemical Engineering, State University of West Parana (2008) (in Portuguese)Google Scholar
  22. Lin, L.C., Juang, R.S.: Ion-exchange equilibria of Cu(II) and Zn (II) from aqueous solutions with Chelex 100 and Amberlite IRC 748 resins. Chem. Eng. J. 112, 211–218 (2005)CrossRefGoogle Scholar
  23. Mishra, V.K., Tripathi, B.D.: Concurrent removal and accumulation of heavy metals by the three aquatic macrophytes. Bioresour. Technol. 99, 7091–7097 (2008)CrossRefGoogle Scholar
  24. Mofidi, N., Moghadam, M.A., Sarbolouki, M.N.: Mass preparation and characterization of alginate microspheres. Process Biochem. 35, 885–888 (2000)CrossRefGoogle Scholar
  25. Mutlu, M., Sag, Y., Kutsal, T.: The adsorption of copper (II) by Z. ramigera immobilized on Ca-alginate in packed bed columns: a dynamic approach by stimulus-response technique and evaluation of adsorption data by moment analysis. Chem. Eng. J. 65, 81–86 (1997)CrossRefGoogle Scholar
  26. Ngah, W.S., Fatinathan, S.: Adsorption of Cu(II) ions in aqueous solution using chitosan beads, chitosan-GLA beads and chitosan-alginate beads. Chem. Eng. J. 143, 62–72 (2008)CrossRefGoogle Scholar
  27. Papageorgiou, S.K., Katsaros, F.K., Kouvelos, E.P., Nolan, J.W., Deit, L.H., Kanellopoulos, N.K.: Heavy metal sorption by calcium alginate beads from Laminaria digitata. J. Hazard. Mater. 137, 1765–1772 (2006)CrossRefGoogle Scholar
  28. Papageorgiou, S.K., Kouvelos, F.K., Katsaros, F.K.: Calcium alginate beads from Laminaria digitata for theremova of Cu2+ and Cd2+ from dilute aqueous metal solutions. Desalination 224, 293–306 (2008)CrossRefGoogle Scholar
  29. Park, H.G., Kim, T.W., Chae, M.Y., Yoo, I.-K.: Activated carbon-containing alginate adsorbent for the simultaneous removal of heavy metals and toxic organics. Process Biochem. 42, 1371–1377 (2007)CrossRefGoogle Scholar
  30. Petrus, R., Warchol, J.K.: Ion exchange equilibria between clinoptilolite and aqueous solutions of Na+/Cu2+, Na+/Cd2+ and Na+/Pb2+. Micropor. Mesopor. Mat. 61, 137–146 (2003)CrossRefGoogle Scholar
  31. Petrus, R., Warchol, J.K.: Heavy metal removal by clinoptilolite. An equilibrium study in multi-component systems. Water Res. 39, 819–830 (2005)CrossRefGoogle Scholar
  32. Pieroni, L.J., Dranoff, J.S.: Ion exchange equilibria in a ternary system. AIChE J. 9(1), 42–45 (1963)CrossRefGoogle Scholar
  33. Poncelet, D., Babak, V., Dulieu, C., Picot, A.: A physico-chemical approach to production of alginate beads by emulsification-internal ionotropic gelation. Colloid Surf. A 55(2–3), 171–176 (1999)CrossRefGoogle Scholar
  34. Prausnitz, J.M., Lichtenthaler, R.N., Azevedo, E.G.: Molecular Thermodynamics of Fluid-Phase Equilibria, 3rd edn, p. 9. Prentice Hall PTR, New Jersey (1999)Google Scholar
  35. Preetha, B., Viruthagiri, T.: Batch and continuous biosorptions of chromium (VI) by Rhizopus arrhizus. Sep. Purif. Technol. 57, 126–133 (2007)CrossRefGoogle Scholar
  36. Quintelas, C., Fernandes, B., Castro, J., Figueiredo, H., Tavares, T.: Biosorption of Cr(VI) by a Bacillus cagulans biofilm supported on granular activated carbon (GAC). Chem. Eng. J. 136, 195–203 (2008)CrossRefGoogle Scholar
  37. Ruthven, D.M.: Principles of Adsorption and Adsorption Process, p. 432. Wiley, New York (1984)Google Scholar
  38. Sag, Y., Kaya, A., Kutsal, T.: The simultaneous biosorption of Cu (II) and Zn on Rhizopus arrhizus: application of the adsorption models. Hydrometallurgy 50, 297–314 (1998)CrossRefGoogle Scholar
  39. Sánchez, A., Ballester, A., Blásquez, M.L., González, F., Muñoz, J., Hammaini, A.: Biosorption of copper and zinc by Cymodocea nodosa. FEMS Microbiol. Rev. 23, 527–536 (1999)CrossRefGoogle Scholar
  40. Sanlder, S.I.: Chemical and Engineering Thermodynamics, 3rd edn, p. 7. Wiley, New York (1999)Google Scholar
  41. Sheng, P.X., Ting, Y.-P., Chen, J.P., Hong, L.: Sorption of lead, copper, cadmium, zinc and nickel by marine algal biomass: characterization of biosorptive capacity and investigation of mechanisms. J. Colloid Interface Sci. 275, 131–141 (2004)CrossRefGoogle Scholar
  42. Silva, F. G. C., Braga, C. G., Lima, L. K. S., Vieira, M. G. A., Silva, M. G. C.: Bioadsorção de Cu2+e Cd2+ utilizando a macrófita aquática Salvinia cucullata. In: Proceedings of Encontro Brasileiro sobre Adsorção (EBA9) & Simpósio Ibero-Americano sobre Adsorção (IBA1), Recife-PE (Itarget) (in Portuguese) (2012)Google Scholar
  43. Silva, V. R.: Obtenção de sericina de alta massa molar mediante extração aquosa e ultrafiltração e a avaliação do seu potencial biossortivo. Doctoral Thesis, Federal University of Parana. Curitiba-PR (2013) (in Portuguese)Google Scholar
  44. Silva, E.A., Cossich, E.S., Tavares, C.R.G., Cardozo Filho, L., Guirardelo, R.: Modeling of copper biosorption by marine alga Sargassum sp. in fixed bed column. Process Biochem. 38, 791–799 (2002)CrossRefGoogle Scholar
  45. Smith, R., Woodburn, W.: Prediction of multicomponent ion exchange equilibria for the ternay system So42–NO3–Cl from data of binary systems. AIChE J. 24, 577–587 (1978)CrossRefGoogle Scholar
  46. Tu, J., Bolla, S., Barr, J., Miedema, J., Li, X., Jasti, B.: Alginate microparticles prepared by spray-coagulation method: preparation, drug loading and release characterization. Int. J. Pharm. 303, 171–181 (2005)CrossRefGoogle Scholar
  47. Veglio, F., Esposito, A., Reverberi, A.P.: Copper adsorption on calcium alginate beads: equilibrium pH-related models. Hydrometallurgy 65, 43–57 (2002)CrossRefGoogle Scholar
  48. Vieira, R. S.: Adsorção competitiva dos íons cobre e mercúrio em membranas de quitosana natural e reticulada. Doctoral Thesis. School of Chemical Engineering - UNICAMP, Campinas-SP (2008) (in Portuguese)Google Scholar
  49. Vieira, M.G.A., Oisiovici, R., Gimenes, M., Silva, M.: Biosorption of chromium(VI) using a Sargassum sp. packed-bed column. Bioresour. Technol. 99, 3094–3099 (2008)CrossRefGoogle Scholar
  50. Vieira, M.G.A., Almeida Neto, A.F., Nóbrega, C.C., Melo Filho, A.A., Silva, M.G.C.: Characterization and use of in natura and calcined rice husks for biosorption of heavy metals ions from aqueous Effluents. Braz. J. Chem. Eng. 29, 619–633 (2012)CrossRefGoogle Scholar
  51. Volesky, B., Kratochvil, D.: Advances in biosorption of heavy metals. Trends Biotechnol. 16, 291–300 (1998)CrossRefGoogle Scholar
  52. Weber Jr, W.J., Wang, C.K.A.: Microscale System for Estimation of Model Parameters for Fixed Bed Adsorbers. Environ. Sci. Technol. 21, 1050–1096 (1987)Google Scholar
  53. Yoshida, H., Yoshikawa, M., Kataoka, T.: Parallel transport of BSA by surface and pore diffusion in strongly basic chitosan. AIChE J. 40, 2034–2044 (1994)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • M. G. C. da Silva
    • 1
  • R. L. S. Canevesi
    • 2
  • R. A. Welter
    • 1
  • M. G. A. Vieira
    • 1
    Email author
  • E. A. da Silva
    • 2
  1. 1.Department of Processes and Product Design, School of Chemical EngineeringUniversity of Campinas, UNICAMPCampinasBrazil
  2. 2.State University of West ParanáToledoBrazil

Personalised recommendations